stats chapter 5 – Flashcards
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If a student is selected at random, what is the probability that this student spends more than $425 on books?
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This cannot be determined from the information given.
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What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students?
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1.0
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A sample of size n is selected at random from a population that has mean ? and standard deviation ?. The sample mean will be determined from the observations in the sample. Which of the following statements about the sample mean, , is (are) TRUE?
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All of the above are true
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Which figure below is most likely a result of sampling the most observations to obtain the distribution of ?
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c.
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What is the sampling distribution of the sample mean score for a random sample of 36 students?
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Exactly Normal.
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The distribution of the sample mean has a standard deviation that is ________ the standard deviation of the distribution of the population from which it was sampled.
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smaller than
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Sodas in a can are supposed to contain an average of 12 ounces. This particular brand has a standard deviation of 0.1 ounces, with an average of 12.1 ounces. If the can's contents follow a Normal distribution, what is the probability that the mean contents of a six-pack are less than 12 ounces?
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0.007
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If the population variable is known to be Normally distributed and the sample size used is to be n = 16, what is the probability that the sample mean will be between 48.35 and 55.74, i.e., P(48.35 ? ? 55.74)?
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0.607
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Which of the following statements is not true?
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A histogram of T-cell velocities would be more Normal if the researchers had collected more data
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The probability that the average age of the 400 trees is more than 60.1 years is
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0.1817
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The lengths of individual fish in a pond have an approximate Normal distribution with a mean of 18.6 cm and a standard deviation of 6.0 cm. A sample of 36 fish is taken. What is the mean of the sampling distribution of the sample mean for the 36 fish?
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18.6 cm
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The variability of a statistic is described by
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the spread of its sampling distribution.
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Cats live for 14 years on average, with a standard deviation of 2 years. A simple random sample of 78 recently deceased cats is selected, and the sample mean age at death of these cats is computed. We know the random variable has an approximately Normal distribution because of
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the central limit theorem
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A quality control manager initially plans to take a simple random sample of size n from the production line. If he were to double his sample size (to 2n), by what factor would the standard deviation of the sampling distribution of change?
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1/ radical 2
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Ten medium oranges will be randomly selected from a package. What is the sampling distribution of the number of oranges in the sample that weigh more than 14 oz?
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B(10, 0.5)
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What is the probability that the average time 100 random students on campus will spend between 1 hour and 5 hours on the internet?
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0.5
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What proportion of tanks will hold between 14.75 and 15.10 gallons of gas?
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0.6997
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What is the variance, , of the sampling distribution of the sample mean, ?
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None of the above
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If the quality control manager takes a simple random sample of ten chocolate bars from the production line, what is the probability that the sample mean weight of the 10 sampled chocolate bars will be less than 8.0 oz?
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0.00078
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If a simple random sample of four tanks is selected, and their capacities can be considered independent, what is the probability that all four will hold between 14.75 and 15.10 gallons of gas?
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0.2397
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We know the random variable has an approximately Normal distribution because of
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the central limit theorem.
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If you take a random sample of 25 vitamin drops, what is, approximately, the probability that the average vitamin content is less than 59.9 mg?
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0.16
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The fact that the sample mean doesn't tend to over- or under-estimate the population mean makes the sample mean
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unbiased.
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If the survey had interviewed only 1000 people, which of the following would be true?
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None of the above
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A statistic here is
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the mean calculated from the 400 trees.
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In order to reduce the standard deviation from the sampling distribution of the sample mean, you should`
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take larger samples
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In the construction industry, compressive strength of concrete is a crucial characteristic. Suppose for a particular residential construction job the concrete tested after 3 days should have a mean compression strength of ? = 3000 psi with a standard deviation of ? = 50 psi. It is known that compressive strength of concrete is Normally distributed. On a construction site, a sample of n = 5 specimens is selected and tested after 3 days. If the concrete has the desired characteristics, what is the probability that the sample mean will be larger than 3060 psi?
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0.004
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The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. If the scores at this school have the same distribution as national scores, the sampling distribution of the average (sample mean) score for the 36 students is
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exactly Normal.
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Based on the central limit theorem, the sampling distribution of the sample mean becomes more normal as the sample siz
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increases
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What is the probability that the average time 100 random students on campus will spend more than 5 hours on the internet?
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0.5
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The probability that the sample mean IQ is greater than 120 is
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0.0790
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If you take a random sample of 25 adult men with liver cirrhosis, what is the probability that their average total body protein is between 9.75 and 9.85 kg?
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0.9876
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If you take a random sample of 25 vitamin drops, what is, approximately, the probability that the average vitamin content is between 60.25 and 60.75 mg?
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0.01
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Considering a sample of 3800 people a large sample, which of the following is true?
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By the central limit theorem, the average amount of gasoline from repeated samples of size 3800 is approximately Normally distributed
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What is the probability that the mean pH measurement of these 4 specimens is greater than 8.2?
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0.0912
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Suppose a simple random sample of 100 observations is to be selected from the population and the sample average, , calculated. Which of the following statements about the distribution of is (are) FALSE?
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Because the distribution shown in the histogram above is clearly skewed to the right, the shape of the distribution of will also show skewness to the right.
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A travel agent randomly selects prices of nonsmoking rooms with a king-size bed from 15 hotels in the area. What is the probability that their average cost will be more than $150?
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0.0077
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From the central limit theorem, we know that if we draw a SRS from any population the sampling distribution of the sample mean will be EXACTLY Normal.
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false
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If a simple random sample of 100 undergraduate students is selected, what is the probability that these students spend, on average, more than $425 on books?
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0.00089
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The central limit theorem says that the sampling distribution of the sample mean is approximately _______ for large n.
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N(u0/radical) the long answer
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he quality control specialist will take a simple random sample of 2000 batteries produced at this plant over the next four days. These batteries will be put into a variety of moderately sized appliances and the average of all failure times will be computed. Which of the following probability distributions is most appropriate to model the average time until failure of these 2000 batteries?
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The Normal distribution
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How big must the sample size n be so that the standard deviation of the sample mean, , is equal to 1.4, i.e., = 1.4?
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n = 115
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Use the 68-95-99.7 rule to answer this question. What is the range of average pH measurements that make up roughly the middle 95% of the sampling distribution for random samples of 4 specimens?
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7.7 to 8.3
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A statistic is said to be unbiased if
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the mean of its sampling distribution is equal to the true value of the parameter being estimated
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Suppose that scores on the Math SAT exam follow a Normal distribution with mean 500 and standard deviation 100. Two students that have taken the exam are selected at random. What is the probability that the sum of their scores exceeds 1200?
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0.0793
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Incomes in a certain town are strongly-right skewed with mean $36000 and standard deviation $7000. A random sample of 10 households is taken. What is the probability the average of the sample is more than $38000?
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Cannot say
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Sample means are more skewed than individual observations.
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false
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Based on the central limit theorem, the sampling distribution of the sample mean becomes more normal as the sample size
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increases
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The quality control manager plans to take a simple random sample of size n from the production line. How big should n be so that the sampling distribution of has standard deviation 0.01 oz?
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100
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Suppose a simple random sample is selected from a population with mean ? and variance ?2. The central limit theorem tells us that
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if the sample size is sufficiently large, the distribution of will be approximately Normal with mean ? and standard deviation,
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The scores of individual students on the American College Testing (ACT) Program College Entrance Exam have a normal distribution with mean 18.6 and standard deviation 6.0. At Westside High, 400 students take the test. Assume their scores are all independent. If the scores at this school have the same distribution as nationally, the probability that the average of the scores of all 400 students exceeds 19.0 is
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smaller than the probability that a single student has a score exceeding 19.0
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Central limit theorem only applies when sampling from Normal populations.
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false
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The distribution of the lengths of all the fish in the lake is the
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population distribution of fish lengths
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If you take a random sample of 25 healthy adult men, what is the probability that their average total body protein is between 12.25 and 12.35 kg?
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0.9876
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Sale of eggs that are contaminated with salmonella can cause food poisoning among consumers. A large egg producer takes an SRS of 200 eggs from all the eggs shipped in one day. The laboratory reports that 11 of these eggs had salmonella contamination. Unknown to the producer, 0.2% (two-tenths of one percent) of all eggs shipped had salmonella. In this situation
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0.2% is a parameter and 11 is a statistic.
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A parameter in this situation is
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the true mean amount of gasoline used the previous week by all people age 18 and older
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The manufacturer of this gasoline tank considers the largest 2% of these tanks too large to put on the market. How large does a tank have to be, to be considered too large?
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15.31 gallons
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A machine fills cans of soda which are labeled "12 ounces" according to a Normal distribution with mean 12.1 ounces and standard deviation 0.1 ounces. If I buy a 12-pack of the soda, what is the chance the average contents of the cans will be less than advertised?
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0.0003
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For the passengers in the SRS, what is the approximate probability that the mean length of time for them to get through security will be less than 18 minutes?
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0.031
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What is the probability that a carton of a dozen eggs weighs more than 13 oz?
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0.0019
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A length of chain is to be constructed by placing 36 component links end-to-end. The length of a link produced by a production process is known to be a random variable with mean ? = 2.5 cm with a standard deviation ? = 0.2 cm. The 36 links are chosen at random from this process to produce the chain. The mean and standard deviation of the length of chain are, respectively
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90 cm, 1.2 cm
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The distribution of the sample mean IQ is
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approximately Normal, mean 118, standard deviation 1.414
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The lengths of individual fish in a pond have an approximate Normal distribution with a mean of 18.6 cm and a standard deviation of 6.0 cm. A sample of 36 fish is taken. What is the standard deviation of the sampling distribution of the sample mean for the 36 fish?
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1.0 cm
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If you take a random sample of 16 healthy adult men, what is the probability that their average total body protein is between 12.25 and 12.35 kg?
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0.9545
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What percentage of nonsmoking rooms with a king-size bed cost more than $150?
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26.60%
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Incomes in a certain town are strongly right-skewed with mean $36000 and standard deviation $7000. A random sample of 75 households is taken. What is the probability the sample mean is greater than $37000?
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0.1075
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The central limit theorem says that, when a simple random sample of size n is drawn from any population with mean ? and standard deviation ?, then when n is sufficiently large
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the distribution of the sample mean is approximately Normal.
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In a simple random sample of 100 undergraduate students, what is the expected value of the sample mean amount of money spent on books?
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$400
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What is the probability that will be less than 1190?
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0.1335
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What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?
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18.6
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A statistic in this situation is
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11.75 gallons
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The central limit theorem does not apply to discrete random variables.
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false
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The sampling distribution of a statistic is
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the distribution of values taken by a statistic in all possible samples of the same size from the same population
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The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a Normal distribution with mean that varies slightly from year to year and standard deviation 6.0. You plan to take an SRS of size n of the students who took the ACT exam this year and compute the mean score of the students in your sample. You will use this to estimate the mean score of all students this year. In order for the standard deviation of to be no more than 0.1, how large should n be?
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at least 3600
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Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8?
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45(0.6)8(0.4)2
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For which of the following does the random variable X have a binomial distribution?
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X is the number of people in a random sample of size 50 from a large population that have type-AB blood.
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A company is being criticized because only 3 of 16 people in executive-level positions are female. The company claims that although the number is lower than it might wish, it is not surprising given the fact that only 40% of their employees are women. Suppose we can consider the 16 people in executive-level positions as a simple random sample of all employees. What is the probability of observing 3 or less women in the group of 16 executives?
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(20/6)(0.42)6(0.58)14
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There are twenty multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth 5 points and only one response per question is correct. Suppose a student guesses the answer to each question, and her guesses from question to question are independent. On average, this strategy will result in a mean score of
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25
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It has been asserted that 15% of all people are left-handed. In a random group of 10 people, what is the chance that not all of them are right-handed
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80.3%
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The probability of success for binomial distribution must remain the same for each observation.
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false
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What is the probability that all students in a simple random sample of 15 students own a cell phone?
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0.206
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If the true proportion of clients who are very satisfied with the Big Smiles Portrait Studio and would therefore recommend the studio to a friend is 82%, what is the probability that more than 60 clients in the sample would answer Yes on the survey question?
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0.0054
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One of the requirements for the binomial distribution is that the observations are all _____.
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independent
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Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that he makes at least 90 free throws?
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.0057
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Mr. Aaron is about to interview four candidates for a certain job. He hopes all the candidates turn off their cell phones, because he does not like to be interrupted by a ringing cell phone. If there is only one candidate whose cell phone rings during the interview, Mr. Aaron will immediately not hire this candidate. If there is only one candidate whose cell phone does not ring during the interview, he will immediately hire this candidate. Suppose all four candidates own cell phones and none turn his/her cell phone off. Each of the candidates will have a 50% chance of being called during their interview. What is the probability that Mr. Aaron will find himself in either one of the two above-described situations: to immediately not hire one candidate because his/her cell phone rang during the interview or to immediately hire one candidate because his/her cell phone was the only one that did not ring during the interview?
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0.50
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A high school has 1000 students. As a school project, the school conducts a mock lottery. Each student in the school is asked to select an integer between 1 and 1000, independently of the choices of the other students. Each student gives their selection, with their name, to the school principal. The school principal uses a random number generator to select an integer between 1 and 1000 and any student that picked this number is declared a winner. What is the probability that no student wins?
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(0.999)1000
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What is the percentage of young adults who do not own a landline?
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75%
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A set of ten cards consists of five red cards and five black cards. The cards are shuffled thoroughly and I am given the first four cards. I count the number of red cards X in these four cards. The random variable X has which of the following probability distributions?
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Neither choice is correct.
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The binomial coefficient, written , gives what information?
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the number of ways in which one can obtain k successes in n trials
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A national poll of 600 men announced that the proportion in the survey who claimed to help their wives at home was 85%. If we took a larger poll of 1200 men, about how many would we expect to say that they help their wives at home, based on the first survey?
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1020
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Six of these cards will be selected at random. Let X = the number of red cards observed in the set of six selected cards. Which of the following probability distributions is appropriate for modeling the random variable X?
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none of the above
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Big Smiles has studios all across the country. Each studio surveys 65 of their clients and records the number of surveyed clients that respond Yes. If a studio scores in the top 6% of the distribution for the number of clients who answer Yes, then the studio will receive an award. Approximately how many clients had to answer Yes on the survey question before the studio will win an award?
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58
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What is the probability that everyone in a simple random sample of 100 young adults owns a landline?
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Less than .001
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Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that the number of free throws he makes exceeds 80?
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.4602
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At the end of a game, his team is losing by two points. He is fouled attempting a three-point shot and is awarded three free throws. Assuming each free throw is independent, what is the probability that he makes at least two of the free throws?
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0.896
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For each of the following scenarios, select if the binomial distribution is the appropriate distribution for the random variable X.
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Five random digits are to be randomly selected from your table of random digits (Table B). Let X = the number of sevens in this set of 5 random digits.
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Suppose we roll a fair six-sided die ten times. What is the probability that even numbers occur exactly the same number of times as do odd numbers on the ten rolls?
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0.2461
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What is the standard deviation of the number of students who own a cell phone in a simple random sample of 15 students?
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1.16
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When a particular penny is held on its edge and spun, the probability that heads are face up when the coin comes to rest is 4/9. If the coin is spun 4 times, the probability that the coin will come up heads exactly twice is (assume trials are independent)
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0.366.
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Which of the following might be reasonably modeled by the binomial distribution?
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Neither choice is correct.
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The binomial distribution is a continuous distribution.
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false
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If the coin is tossed six times, what is the probability that less than ? of the tosses are heads?
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0.109
