Section 6.1 and 6.2 exercises Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A normal population has a mean μ = 30 and standard deviation σ = 7. What is the probability that a randomly chosen value will be greater than 31? A) 0.7881 B) 0.5557 C) 0.4443 D) 0.7580 2) A fast-food restaurant chain has 623 outlets in the United States. The following table categorizes them by city population and location and presents the number of outlets in each category. An outlet is chosen at random from the 623 to test market a new menu. 1) 2) Region Population of city NE SE SW NW Under 50,000 30 26 27 19 50,000-500,000 60 48 50 39 Over 500,000 72 125 79 48 Given that the outlet is located in a city with a population under 50,000, what is the probability that it is in the Southwest? A) 0.255 B) 0.265 C) 0.164 D) 0.043 3) Find the z-scores that bound the middle 74% of the area under the standard normal curve. A) -1.07, 1.07 B) -1.13, 1.13 C) -1.24, 1.24 D) -0.99, 0.99 3) Find the indicated probability. 4) The table below describes the smoking habits of a group of asthma sufferers. 4) Light Heavy Nonsmoker smoker smoker Total Men 395 63 79 537 Women 363 86 67 516 Total 758 149 146 1053 What is the probability that a woman is a nonsmoker? A) 0.345 B) 0.49 C) 0.720 D) 0.479 E) 0.703 1
5) You are dealt a hand of three cards, one at a time. Find the probability that your cards are all diamonds. A) 0.231 B) 0.013 C) 0.750 D) 0.016 E) 0.705 5) 6) The table below describes the smoking habits of a group of asthma sufferers. 6) Light Heavy Nonsmoker smoker smoker Total Men 331 65 61 457 Women 358 65 86 509 Total 689 130 147 966 What is the probability that a light smoker is a woman? A) 0.135 B) 0.128 C) 0.067 D) 0.5 E) 0.713 7) An IRS auditor randomly selects 3 tax returns from 54 returns of which 10 contain errors. What is the probability that she selects none of those containing errors? A) 0.006 B) 0.541 C) 0.534 D) 0.005 E) 0.466 8) A box contains 12 batteries of which 5 are still working. Anne starts picking batteries one at a time from the box and testing them. Find the probability that she has to pick 5 batteries in order to find one that works. A) 6.031 B) 0.013 C) 0.017 D) 0.044 E) 0.001 9) You are dealt a hand of three cards, one at a time. Find the probability that your third card is your first ace. A) 0.127 B) 0.00018 C) 0.068 D) 0.077 E) 0.145 10) Find the area under the standard normal curve to the left of z = -0.7. A) 0.1210 B) 0.2420 C) 0.7580 D) 0.2580 11) Find the area under the standard normal curve to the right of z = 1.6. A) 0.0548 B) 0.0274 C) 0.9452 D) 0.4452 12) The mean number of pets per household is 3.25 with standard deviation 1.3. A sample of 59 households is drawn. Find the 74th percentile of the sample mean. A) 3.36 B) 2.70 C) 3.86 D) 4.11 7) 8) 9) 10) 11) 12) Solve the problem. Round to the nearest tenth. 13) For a recent English exam, use the Normal model N(73, 9.2) to find the score that represents the 90th percentile. A) 84.8 B) 63.8 C) 61.2 D) 82.2 E) 81.3 13) 2
14) For a recent English exam, use the Normal model N(73, 9.2) to find the score that represents the 30th percentile. A) 61.2 B) 63.8 C) 82.2 D) 77.8 E) 68.2 15) Based on the Normal model for car speeds on an old town highway N(77, 9.1), what is the cutoff value for the highest 15% of the speeds? A) about 63.1 mph B) about 65.5 mph C) about 11.6 mph D) about 67.5 mph E) about 86.5 mph 16) A fast-food restaurant chain has 617 outlets in the United States. The following table categorizes them by city population and location and presents the number of outlets in each category. An outlet is chosen at random from the 617 to test market a new menu. 14) 15) 16) Region Population of city NE SE SW NW Under 50,000 32 32 26 16 50,000-500,000 50 41 56 40 Over 500,000 76 125 78 45 Given that the outlet is located in the West (either SW or NW), what is the probability th it is in a city with population 50,000 500,000? A) 0.156 B) 0.368 C) 0.268 D) 0.716 Solve the problem. 17) A bankʹs loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, what percentage can be expected to be between 200 and 275? A) 43.32% B) 5.00% C) 6.68% D) 93.32% E) 42.37% 18) For a recent English exam, use the Normal model N(73, 9.2) to find the percent of scores over 85. Round to the nearest tenth of a percent. A) 9.7% B) 11.5% C) 88.5% D) 8.1% E) 90.3% 19) The lengths of human pregnancies can be described by a Normal model with a mean of 268 days and a standard deviation of 15 days. What percentage can we expect for a pregnancy that will last at least 300 days? A) 98.34% B) 1.79% C) 1.66% D) 1.99% E) 48.34% 17) 18) 19) 3
20) The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume less than 32 oz? A) 9.87% B) 40.13% C) 47.15% D) 59.87% E) 38.21% 21) A townʹs average snowfall is 46 inches per year with a standard deviation of 10 inches. Using a Normal model, what values should border the middle 68% of the model? A) 48 inches and 44 inches B) 66 inches and 26 inches C) 46 inches and 42.6 inches D) 56 inches and 36 inches E) 51 inches and 41 inches 22) The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.6 pounds and standard deviation 1.9 pounds. A turkey farmer wants to provide a money-back guarantee that her 6-week poults will weigh at least a certain amount. What weight should she guarantee so that she will have to give her customer's money back only 1% of the time? A) 4.17 lb B) 5.00 lb C) 3.34 lb D) 4.59 lb 23) A normal population has a mean μ = 34 and standard deviation σ = 11. What proportion of the population is less than 41? A) 0.2611 B) 1.0000 C) 0.7389 D) 0.8106 24) A normal population has a mean μ = 27 and standard deviation σ = 9. What proportion of the population is between 26 and 31? A) 0.6700 B) 0.2138 C) 0.4562 D) 0.7862 25) Find the z-score for which the area to the right is 0.07. A) 1.59 B) 1.48 C) 1.35 D) 1.74 26) A bottler of drinking water fills plastic bottles with a mean volume of 994 milliliters (ml) and standard deviation 5 ml. The fill volumes are normally distributed. What proportion of bottles have volumes less than 995 ml? A) 0.5793 B) 0.9974 C) 0.5596 D) 1.0000 27) A normal population has a mean μ = 10 and standard deviation σ = 2. What is the 86th percentile of the population? A) 13.38 B) 12.16 C) 10.94 D) 9.73 20) 21) 22) 23) 24) 25) 26) 27) 4
28) A sample of size 40 will be drawn from a population with mean 98 and standard deviation 24. Find the 21st percentile of x. A) 93.8 B) 90.8 C) 94.9 D) 91.4 28) 29) Find the area under the standard normal curve that lies between z = 1.8 and z = 2. A) 0.4772 B) 0.0132 C) 0.5228 D) 0.9868 29) 30) The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the slips are placed into a hat. If the slips are drawn randomly without replacement, what is the probability that "A" is drawn first and "B" is drawn second? A) 0.033 B) 0.039 C) 0.024 D) 0.028 30) 31) A sample of size 42 will be drawn from a population with mean 34 and standard deviation 8. Find the probability that x will be greater than 36. A) 0.0351 B) 0.0749 C) 0.0526 D) 0.9474 31) 32) A certain car model has a mean gas mileage of 29 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 38 of these cars. What is the probability that the average mileage of the fleet is greater than 27.8 mpg? A) 0.9535 B) 0.8599 C) 0.0465 D) 0.9306 32) 33) The mean annual income for people in a certain city (in thousands of dollars) is 38, with a standard deviation of 31. A pollster draws a sample of 43 people to interview. Find the 68th percentile of the sample mean. A) 40.2 thousand dollars B) 37.7 thousand dollars C) 38.7 thousand dollars D) 42.3 thousand dollars 33) 5
Answer Key Testname: SECTIONS 4.3, 6.1, 6.2 AND 6.3 IN CLASS EXERCISES 1) C 2) B 3) B 4) E 5) B 6) D 7) C 8) D 9) C 10) B 11) A 12) A 13) A 14) E 15) E 16) B 17) A 18) A 19) C 20) B 21) D 22) A 23) C 24) B 25) B 26) A 27) B 28) C 29) B 30) A 31) C 32) D 33) A 6