Business Statistics: Chapter 7 Quiz Flashcards
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37. The shape of any uniform probability distribution is
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A) Negatively skewed B) Positively skewed C) Rectangular D) Bell shaped Answer: C
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38. The mean of any uniform probability distribution is
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A) (b - a)/2 B) (a + b)/2 C) D) n Answer: B
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39. The standard deviation of any uniform probability distribution is
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A) (b - a)/2 B) n ( 1 - ) C) D) Answer: C
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40. The upper and lower limits of a uniform probability distribution are
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A) positive and negative infinity B) plus and minus three standard deviations. C) 0 and 1 D) the maximum and minimum values of the random variable. Answer: D
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41. When using the binomial distribution to approximate a normal distribution, what is the
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value of the continuity correction factor? A) 1.00 B) 0.50 C) 100 D) 1.96 Answer: B
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42. A new drug relieves nasal congestion in 90 percent of those with the condition. The new drug is administered to 300 patients with the condition. What is the probability that more than 265 will be relieved of nasal congestion?
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A) 0.0916 B) 0.1922 C) 0.8078 D) 0.3078 Answer: C
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43. What is an important similarity between the uniform and normal probability distributions?
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A) The mean, median and mode are all equal. B) The mean and median are equal C) They are negatively skewed D) About 68% of all observations are within one standard deviation of the mean. Answer: B
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44. Which of the following is NOT true regarding the normal distribution?
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A) Mean, median and mode are all equal B) It has a single peak C) It is symmetrical D) The points of the curve meet the X-axis at z = -3 and z = 3 Answer: D
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45. For the normal distribution, the mean plus and minus 1.96 standard deviations will include about what percent of the observations?
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A) 50% B) 99.7% C) 95% D) 68% Answer: C
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46. For a standard normal distribution, what is the probability that z is greater than 1.75?
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A) 0.0401 B) 0.0459 C) 0.4599 D) 0.9599 Answer: A
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47. What is the area under the normal curve between z = 0.0 and z = 1.79?
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A) 0.4633 B) 0.0367 C) 0.9599 D) 0.0401 Answer: A
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48. What is the area under the normal curve between z = -1.0 and z = -2.0?
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A) 0.0228 B) 0.3413 C) 0.1359 D) 0.4772 Answer: C
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49. What is the area under the normal curve between z = 0.0 and z = 2.0?
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A) 1.0000 B) 0.7408 C) 0.1359 D) 0.4772 Answer: D
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50. The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. Assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month?
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A) 0.2158 B) 0.8750 C) 0.0362 D) 0.1151 Answer: D
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51. Which of the following is NOT a characteristic of the normal probability distribution?
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A) Positively-skewed B) Bell-shaped C) Symmetrical D) Asymptotic Answer: A
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52. What is the proportion of the total area under the normal curve within plus and minus two standard deviations of the mean?
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A) 68% B) 99.7% C) 34% D) 95% Answer: D
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53. The mean score of a college entrance test is 500; the standard deviation is 75. The scores are normally distributed. What percent of the students scored below 320?
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A) About 50.82% B) About 34.13% C) About 7.86% D) About 0.82% Answer: D
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54. The mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100. What is the z-score for an income of $1,100?
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A) 1.00 B) 2.00 C) 1.683 D) -0.90 Answer: A
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55. A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. If the service life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours?
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A) 95% B) 68% C) 34% D) 99.7% Answer: D
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56. A study of a company's practice regarding the payment of invoices revealed that an invoice was paid an average of 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt?
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A) 15.87% B) 37.91% C) 34.13% D) 86.74% Answer: A
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57. An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before they failed is 19.0 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.2 hours. About 95.44 percent of the batteries failed between what two values?
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A) 8.9 and 18.9 B) 12.2 and 14.2 C) 14.1 and 22.1 D) 16.6 and 21.4 Answer: D
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58. The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds?
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A) 0.5000 B) 0.1932 C) 0.4332 D) 0.3413 Answer: C
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59. The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68 percent of the incomes lie between what two incomes?
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A) $30,000 and $40,000 B) $36,400 and $38,000 C) $34,800 and $39,600 D) $35,600 and $38,800 Answer: B
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60. Which of the following is true in a normal distribution?
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A) Mean equals the mode and the median B) Mode equals the median C) Mean divides the distribution into two equal parts D) All of the above are correct Answer: D
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61. Tables of normal distribution probabilities are found in many statistics books. These probabilities are calculated from a normal distribution with
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A) a mean of 1 and a standard deviation of 1 B) a mean of 100 and a standard deviation of 15 C) a mean of 0 and a standard deviation of 15 D) a mean of 0 and a standard deviation of 1 Answer: D
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62. Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second normal distribution has a mean of 10 and a standard deviation of 2. Which of the following it true?
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A) the locations of the distributions are different B) the distributions are from two different families C) the dispersions of the distributions are different D) the dispersions of the distributions are the same Answer: C
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63. A random variable from an experiment where outcomes are normally distributed
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A) can have any value between - and + B) can have only a few discrete values C) can have a mean of 0 and a standard deviation of 1 D) can have no values Answer: A
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64. The total area of a normal probability distribution is
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A) between -3.0 and 3.0 B) 1.00 C) dependent on a value of 'z'. D) approximated by the binomial distribution. Answer: B
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65. An area of a normal probability distribution represents
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A) a permutation B) a combination C) a likelihood D) a shaded area Answer: C
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66. The standard normal probability distribution is one which has:
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A) A mean of 1 and any standard deviation B) Any mean and a standard deviation of 1 C) A mean of 0 and any standard deviation D) A mean of 0 and a standard deviation of 1 Answer: D
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67. The weekly mean income of a group of executives is $1000 and the standard deviation of this group is $100. The distribution is normal. What percent of the executives have an income of $925 or less?
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A) About 15% B) About 85% C) About 50% D) About 23% Answer: D
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68. The weight of cans of fruit is normally distributed with a mean of 1,000 grams and a standard deviation of 50 grams. What percent of the cans weigh 860 grams or less?
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A) 0.0100 B) 0.8400 C) 0.0026 D) 0.0001 Answer: C
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69. What is the distribution with a mean of 0 and a standard deviation of 1 called?
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A) Frequency distribution B) z-score C) Standard normal distribution D) Binomial probability distribution Answer: C
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70. The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 15.0 pounds, and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing between 13 and 16 pounds?
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A) 100 B) 118 C) 197 D) 53 Answer: B
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71. Ball-Bearings, Inc. produces ball bearings automatically on a Kronar BBX machine. For one of the ball bearings, the mean diameter is set at 20.00 mm (millimeters). The standard deviation of the production over a long period of time was computed to be 0.150 mm. What percent of the ball bearings will have diameters 20.27 mm or more?
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A) 41.00% B) 12.62% C) 3.59% D) 85.00% Answer: C
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72. A national manufacturer of unattached garages discovered that the distribution of the lengths of time it takes two construction workers to erect the Red Barn model is approximately normally distributed with a mean of 32 hours and a standard deviation of 2 hours. What percent of the garages take between 30 and 34 hours to erect?
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A) 16.29% B) 76.71% C) 3.14% D) 34.13% Answer: D
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73. A large manufacturing firm tests job applicants who recently graduated from college. The test scores are normally distributed with a mean of 500 and a standard deviation of 50. Management is considering placing a new hire in an upper level management position if the person scores in the upper 6 percent of the distribution. What is the lowest score a college graduate must earn to qualify for a responsible position?
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A) 50 B) 625 C) 460 D) 578 Answer: D
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74. An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8. The instructor wants to award the grade of A to the upper 10 percent of the test grades. What is the dividing point between an A and a B grade?
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A) 80 B) 85 C) 90 D) 95 Answer: B
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75. The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000. What percent of the sales persons earn between $32,000 and $42,000?
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A) 60.06% B) 39.94% C) 34.13% D) 81.66% Answer: A
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76. The mean of a normal probability distribution is 500 and the standard deviation is 10. About 95 percent of the observations lie between what two values?
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A) 475 and 525 B) 480 and 520 C) 400 and 600 D) 350 and 650 Answer: B
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77. A cola-dispensing machine is set to dispense a mean of 2.02 liters into a container labeled 2 liters. Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 liters. What is the probability a container will have less than 2 liters?
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A) 0.0918 B) 0.3413 C) 0.1926 D) 0.8741 Answer: A
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78. The employees of Cartwright Manufacturing are awarded efficiency ratings. The distribution of the ratings approximates a normal distribution. The mean is 400, the standard deviation 50. What is the area under the normal curve between 400 and 482?
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A) 0.5000 B) 0.4495 C) 0.3413 D) 0.4750 Answer: B
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79. Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Tests revealed that the tire's mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 5 percent of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce?
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A) 44,528 B) 32,960 C) 49,621 D) 40,922 Answer: A
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80. The mean amount of gasoline and services charged by Key Refining Company credit customers is $70 per month. The distribution of amounts spent is approximately normal with a standard deviation of $10. What is the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83?
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A) 0.1962 B) 0.4032 C) 0.3413 D) 0.4750 Answer: B
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81. Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 percent of production based on past experience. Past records indicate that, on the average, 4,000 units of a small assembly are produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. If the bonus is paid on the upper 5 percent of production, the bonus will be paid on how many units or more?
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A) 6255 B) 5120 C) 3196 D) 4099 Answer: D
