Stats 1 Exam 2 – Flashcards
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The outcome of an experiment is the number of resulting heads when a nickel and a dime are flipped simultaneously. a) what is the sample space for this experiment b) what is the sample space is the outcome of the experiment is recording the face up.
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a) {0,1,2} b) {HH, HT, TH, TT}
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A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple event and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc) Simple Events Probabilities SS 0.52 SD 0.15 DS 0.11 DD 0.22 Find the probability that both patients survive
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0.52
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A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple event and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc) Simple Events Probabilities SS 0.59 SD 0.10 DS 0.16 DD 0.15 Find the probability that at least one of the patients does not survive
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0.41
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A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple event and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc) Simple Events Probabilities SS 0.54 SD 0.14 DS 0.19 DD 0.13 Find the probability that neither patient survives
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0.13
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Each manager of a Fortune 500 company was rated as being either a good, fair or poor manager by his/her boss. The manager's educational backround was also noted. The date appears below Managers Rating H.S. Deg. Some Coll. Coll. Deg. M/PHD Tot Good 7 4 22 6 39 Fair 8 19 49 11 87 Poor 3 5 6 20 34 Total 18 28 77 37 160 What is the probability that a randomly chosen manager has earned at least one college degree?
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57/80
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Each manager of a corporation was rated as being either a good, fair or poor manager by his/her boss. The manager's educational backround was also noted. The date appears below Managers Rating H.S. Deg. Some Coll. Coll. Deg. M/PHD Tot Good 9 3 23 4 39 Fair 5 19 43 20 87 Poor 2 8 4 20 34 Total 16 30 70 44 160 If we randomly selected one manager from this company, fin the probability that he or she has an advanced (M or PH.D) degree and is a good manager.
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1/40
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Four Hundred accidents that occurred on a saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown below: Did Alcohol Play a Role 1 2 3^ Totals Yes 57 92 21 170 No 24 172 34 230 Totals 81 264 55 400 Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident involved more than a single vehicle.
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319/400
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A clothing vendor estimated that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is that probability that a randomly selected online customer lives within 50 miles of a physical store?
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0.22
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In a sample of 750 of its online customers, a department store found that 420 were men. use this information to estimate the probability that a randomly selected online customer is not a man.
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0.44
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At a small private college with 800 students, 240 students recieve some form of governement-sponsored financial aid. Find the probability that a randomly selected student does not recieve a form of financial aid.
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0.70
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A number between 1 & 10, inclusive is randomly chosen. Events A,B,C & D are defined as follows S={1,2,3,4,5,6,7,8,9,10} a: (The number is even) b: (The number is less than 7) c: ( The number is odd) d: (the number is greater than 5 Identify one pair of mutually exclusive events Identify one pair of independent events
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a:{2,4,6,8,10} -> P(a)= 5/10 b:{1,2,3,4,5,6} -> P(b)= 6/10 c: {1,3,5,7,9} -> P(c)= 5/10 d: {6,7,8,9,10} -> P(d)= 5/10 A & C are mutually exclusive event because A∩C don't have points in common
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2 chips are drawn at random and without replacement from a bag containing 2 blue chips and 2 red chips a) both chips are red b) atleast one chip is blue Are the events A & B mutually exclusive? Indentify one pair of independent events
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a) RR b) RB, BR,BB A∩B have no sample points in common so it IS mutually exclusive They are independent
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Suppose that for a certain experiment P(a)=0.47 and P(b)=0.25 and P(A∩B)=0.14. Find P(A U B)
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0.58
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In a class of 30 students 18 are men, 6 are earning a B and 2 men are earning a B. If a student is randomly selected from the class, find the probability that the student is a man earning a B?
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0.73
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In a box of 75 markers, 36 markers are either red or black and 15 are blue. Find the probability that a randomly selected market is red, black or blue.
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0.68
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A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the probability that a yellow or pink notepad is selected given that it is either blue or green
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P(yellow "or" pink)/blue or"green) = 0/12 = 0
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An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, an 3 orange highlighters. An experiment consists of randomly selecting one the highlighters and recording its color. Find the probability that a bllue or yellow highlighter is selected given that a yellow highlighter is selected
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P(blue "or" yellow)/yellow=12/12 = 1
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Suppose that for a certain experiment P(a) = 0.6, P(b) = 0.3. If A and B are independent events find P(A∩B)
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0.18
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Suppose that for a certain experiment P(A) = .15 and P(B|A) = 0.8. Find P(A∩B)
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0.120
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Supposed that for a certain experiment P(a)= .32, P(b)= .55. If A and B are independent events, find P(A∩B)
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0.176
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The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Suppose that the die is rolled once Outcome 1 2 3 4 5 6 Probability .1 .1 .1 .2 .2 .3 Events A, B, C, & D are defined as follows A{The number is even} B{The number is less than 4} C{ The number is less than or equal to 5} D{The number is greater than or equal to 5} Identify one pair of independent events.
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A{2,4,6}; P(A) = 0.6 B{1,2,3}; P(B) = 0.3 C{1,2,3,4,5} P(C)= 0.7 D{5,6}=P(D) = 0.5 A∩D= 0.3 IT IS INDEPENDENT
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Classify the following random variable according to whether it is a discrete or continuous. The height of a plater on a basketball team
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Continuous
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Classify the following random variable according to whether it is a discrete or continuous. The temperature in degrees fahrenheit on July 4th in Juneau, Alaska
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Continuous
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Classify the following random variable according to whether it is a discrete or continuous. The number of goals scored in a soccer game
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Discrete
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Classify the following random variable according to whether it is a discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day.
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Discrete
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Explain why the following is or is not a valid probability distribution for the discrete random variable x x 1 0 1 2 3 p(x) .1 .2 .3 .3 .1
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Yes because .1+.2+.3+.3+.1=1
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Explain why the following is or is not a valid probability distribution for the discrete random variable x x 0 2 4 6 8 p(x) - .1 .1 .2 .3 .5
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No because the "-.1" has no probability value
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Explain why the following is or is not a valid probability distribution for the discrete random variable x x 10 20 30 40 50 p(x) .3 .2 .2 .2 .2
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No because the summation of p(x) = 1.1 and not 1
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Consider the given discrete probability distribution. Find the probability that X equals 5 x 2 5 6 9 p(x) 0.09 ? .23 0.21
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0.47
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Consider the given discrete probability distribution. Find the probability that X exceeds 5 x 3 5 7 9 p(x) 0.24 ? .26 0.01
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0.27
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Consider the given discrete probability distribution. Find P(x ≤ 4). B: (1 ≤ x 3) x 0 1 2 3 4 5 p(x) .30 .25 .20 .15 .05 .05
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a) 0.95 b)0.6 c)0.10
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A local bakery has determinded a probability distribution for the number of cheesecakes it sells in a given day. The distribution is as follows # sold in a day 0 5 10 15 20 Prob(# sold) 0.21 0.15 0.06 0.07 0.51 Find the number of cheesecakes that this local bakery expects to sell in a day
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12.6
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Mamma Temte bakes 6 pies each day at a cost $2 each. On 24% of the days she sells only two pies. On 22% of the days, she sells 4 pies and on the remaining 54% of the days, she sells all 6 pies. If Mamma Temte sells her pies for 6$ each, what is her expected profit fora day's worth of pies?
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$15.60
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The random variable x represents the number of boys in a family with three children. Assuming that births of boys and girls are equally likely, find the mean and standard deviation for the random variable x
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Mean: 1.50; StDev = .87
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Find the mean and standard deviation of the probability distributor for the random variable x, which represents the number of cars per household in a small town x p(x) 0 .125 1 .428 2 .256 3 .108 4 .083
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check answer for work mean: 1.596 StDev: 1.09
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Calculate the mean and varience for the discrete probability distribution shown here. x 2 5 7 9 p(x) .2 .3 .3 .2
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Check answers for work Mean: 5.8 VAR: 5.56
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For a binomial distribution, if the probability of success is .48 on the first trial, what is the probability of failure on the second trial?
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p(failure) = 0.52
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For a binomial distribution, if the probability of success is .53 on the first trial, what is the probability of success on the second trial?
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p(success) = 0.53
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According to a recent study 4 in every 8 women has been a victime of domestic abuse at some point in her life. Suppose 25 women are asked each whether she has been a cistim of domestic abuse at some point in her life. a) Find the probability that more than 23 of the women sampled have no been victim b) find the probability that at most 3 have been victims c) Find the probability that at least 4 have been victims
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A) = 0 B) = 0 C) = 1
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We believe that 90% of the population of all business Statistics 1 students consider statistics to be an exciting subject. Suppose we randomly and independently selected 25 students from the population. If the true percentage is really 90% a) Find the probability of observing 22 or more students who consider statistics to be an exciting subject. b) Find the probability at most 17 students consider statitistics to be an exciting subject c) Find the probability of observing at least 18 students who consider statistics to be an exciting subject.
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A) = 0.764 b) = 0 C) = 0.998
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A recent survery found that 63% of all adults over 50 wear glasses for driving. In a random sample of 10 adults over 50, what is the mean of Standard deviation of the number who wear glasses
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mean: 6.3 St Dev: 1.53
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According to a published study 1 in every 8 men has been involved in a minor traffic accident. Supposed we have randomly and independently sampled 25 men and asked each whether he was involved in a minor traffic accident. How many of the 25 men do we expect to have never been involved in an accident.
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mean = 3.125
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We believe that 81% of the population of all business Statistics 1 students consider statistics to be an exciting subject. Suppose we randomly and independently selected 39 students from the population. How many of the sampled students do we expect to consider stats an exciting subject?
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mean = 31.59
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A pair of fair dice is tosse Events A & B are as follows a: {The two numbers rolled are odd} b: {The sum of the numbers showing is } 2, 11, 12} Find the probability of the following events a) P (A U B) b) P (A∩B) c) P (B/A)
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A: 9 outcomes B: 4 outcomes a)= 1/3 b) = 1/36 c)= 1/9
