MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response.

Transcription

1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Find the area of the indicated region under the standard normal curve. 1) A) B) C) D) ) Find the area of the indicated region under the standard normal curve. 2) A) B) C) D) ) Find the area of the indicated region under the standard normal curve. 3) A) B) C) D) ) Find the area of the indicated region under the standard normal curve. 4) A) B) C) D) ) Find the area under the standard normal curve to the left of z = 1.5. A) B) C) D) ) 6) Find the area under the standard normal curve to the left of z = A) B) C) D) ) 1

2 7) Find the area under the standard normal curve to the right of z = 1. A) B) C) D) ) 8) Find the area under the standard normal curve to the right of z = A) B) C) D) ) 9) Find the area under the standard normal curve between z = 0 and z = 3. A) B) C) D) ) 10) Find the area under the standard normal curve between z = 1 and z = 2. A) B) C) D) ) 11) Find the area under the standard normal curve between z = -1.5 and z = 2.5. A) B) C) D) ) 12) Find the area under the standard normal curve between z = 1.5 and z = 2.5. A) B) C) D) ) 13) Find the area under the standard normal curve between z = and z = A) B) C) D) ) 14) Find the sum of the areas under the standard normal curve to the left of z = and to the right of z = A) B) C) D) ) 15) Find the area of the indicated region under the standard normal curve. 15) A) B) C) D) ) Find the area of the indicated region under the standard normal curve. 16) A) B) C) D)

3 17) Find the area of the indicated region under the standard normal curve. 17) A) B) C) D) ) Find the area of the indicated region under the standard normal curve. 18) A) B) C) D) ) Find the area under the standard normal curve to the left of z = 1.5. A) B) C) D) ) 20) Find the area under the standard normal curve to the left of z = A) B) C) D) ) 21) Find the area under the standard normal curve to the right of z = 1. A) B) C) D) ) 22) Find the area under the standard normal curve to the right of z = A) B) C) D) ) 23) Find the area under the standard normal curve between z = 0 and z = 3. A) B) C) D) ) 24) Find the area under the standard normal curve between z = 1 and z = 2. A) B) C) D) ) 25) Find the area under the standard normal curve between z = -1.5 and z = 2.5. A) B) C) D) ) 26) Find the area under the standard normal curve between z = 1.5 and z = 2.5. A) B) C) D) ) 27) Find the area under the standard normal curve between z = and z = A) B) C) D) ) 28) Find the sum of the areas under the standard normal curve to the left of z = and to the right of z = A) B) C) D) ) 3

4 Find the probability of z occurring in the indicated region. 29) 29) z A) B) C) D) ) 30) z A) B) C) D) ) 31) z A) B) C) D)

5 32) 32) z A) B) C) D) ) 33) z A) B) C) D) ) 34) z A) B) C) D)

6 Provide an appropriate response. 35) Use the standard normal distribution to find P(0 < z < 2.25). A) B) C) D) ) 36) Use the standard normal distribution to find P(-2.25 < z < 0). A) B) C) D) ) 37) Use the standard normal distribution to find P(-2.25 < z < 1.25). A) B) C) D) ) 38) Use the standard normal distribution to find P(-2.50 < z < 1.50). A) B) C) D) ) 39) Use the standard normal distribution to find P(z < or z > 2.33). A) B) C) D) ) 40) For the standard normal curve, find the z-score that corresponds to the third quartile. A) 0.67 B) 0.77 C) D) ) 41) For the standard normal curve, find the z-score that corresponds to the first quartile. A) B) 0.77 C) 0.67 D) ) 42) For the standard normal curve, find the z-score that corresponds to the first decile. A) 1.28 B) C) D) ) Provide an appropriate response. Use the Standard Normal Table to find the probability. 43) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 110. Find the z-score corresponding to this value. A) 0.67 B) C) D) ) 44) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 90. Find the z-score corresponding to this value. A) B) 1.33 C) D) ) 45) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 120. Find the z-score corresponding to this value. A) B) 0.67 C) 1.33 D) ) 46) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the IQ score that corresponds to a z-score of A) B) C) D) ) 47) IQ test scores are normally distributed with a mean of 102 and a standard deviation of 19. An individualʹs IQ score is found to be 124. Find the z-score corresponding to this value. A) B) 1.16 C) 0.86 D) ) 48) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 12. An individualʹs IQ score is found to be 127. Find the z-score corresponding to this value. A) 2.25 B) 0.44 C) D) ) 6

7 49) The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting more than 300 days. A) B) C) D) ) 50) The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting less than 250 days. A) B) C) D) ) 51) The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and σ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. Find the probability that a teenage boy has a cholesterol level greater than 200. A) B) C) D) ) 52) The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and σ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. Find the probability that a teenage boy has a cholesterol level greater than 225. A) B) C) D) ) 53) An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given week the airline will lose less than 20 suitcases? A) B) C) D) ) 54) An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given week the airline will lose more than 20 suitcases? A) B) C) D) ) 55) An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given week the airline will lose between 10 and 20 suitcases? A) B) C) D) ) 56) Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that he or she makes more than $36,000. A) B) C) D) ) 57) Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that he or she makes less than $28,000. A) B) C) D) ) 58) Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. The cheerleaders for a local professional basketball team must be between 65.5 and 68.0 inches. If a woman is randomly selected, what is the probability that her height is between 65.5 and 68.0 inches? A) B) C) D) ) 7

8 59) The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. A baby is premature if it is born three weeks early. What percent of babies are born prematurely? A) 8.08% B) 9.21% C) 6.81% D) 10.31% 59) 60) The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and σ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. What percent of teenage boys have levels between 170 and 225? A) 3.36% B) 46.64% C) 56.13% D) 6.06% 60) 61) Assume that blood pressure readings are normally distributed with μ= 120 and σ = 8. A blood pressure reading of 145 or more may require medical attention. What percent of people have a blood pressure reading greater than 145? A) 99.91% B) 0.09% C) 11.09% D) 6.06% 61) 62) Assume that the heights of American men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between 64 and 78 inches. Find the percent of men meeting these height requirements. A) 96.26% B) 31.12% C) 99.93% D) 3.67% 62) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 63) Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. The U.S. Army requires that the heights of women be between 58 and 80 inches. If a woman is randomly selected, what is the probability that her height is between 58 and 80 inches? 63) 64) The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Out of 50 pregnancies, how many would you expect to last less than 250 days? 64) 65) The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and σ = 30. Levels above 200 warrant attention. If 95 teenage boys are examined, how many would you expect to have cholesterol levels greater than 225? 65) 66) An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. In one year, how many weeks would you expect the airline to lose between 10 and 20 suitcases? 66) 67) Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. The U.S. Army requires that the heights of women be between 58 and 80 inches. If 200 women want to enlist in the U.S. Army, how many would you expect to meet the height requirements? 67) 68) Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that the heights of men be between 64 and 78 inches. If 500 men want to enlist in the U.S. Marine Corps, how many would you not expect to meet the height requirements? 68) 8

9 Provide an appropriate response. 69) Find the z-score that corresponds to the given area under the standard normal curve. 69) 70) Find the z-score that corresponds to the given area under the standard normal curve. 70) 71) Find the z-score that corresponds to the given area under the standard normal curve. 71) 72) Find the z-score that corresponds to the given area under the standard normal curve. 72) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 73) Find the z-scores for which 90% of the distributionʹs area lies between -z and z. A) (-0.99, 0.99) B) (-1.645, 1.645) C) (-1.96, 1.96) D) (-2.33, 2.33) 73) 74) Find the z-scores for which 98% of the distributionʹs area lies between -z and z. A) (-0.99, 0.99) B) (-1.645, 1.645) C) (-1.96, 1.96) D) (-2.33, 2.33) 74) 75) Find the z-score for which 70% of the distributionʹs area lies to its right. A) B) C) D) ) 76) Find the z-score that is greater than the mean and for which 70% of the distributionʹs area lies to its left. A) 0.47 B) 0.81 C) 0.53 D) ) 9

10 77) Use a standard normal table to find the z-score that corresponds to the cumulative area of A) B) C) 0.53 D) ) 78) Find the z-score that has 93.82% of the distributionʹs area to its right. A) B) C) D) ) 79) Find the z-score for which 99% of the distributionʹs area lies between -z and z. A) (-2.575, 2.575) B) (-2.33, 2.33) C) (-1.645, 1.645) D) (-1.96, 1.96) 79) 80) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of A) B) C) D) ) 81) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of A) 82.3 B) 91.0 C) 75.3 D) ) 82) The scores on a mathematics exam have a mean of 77 and a standard deviation of 8. Find the x-value that corresponds to the z-score A) 56.4 B) 79.6 C) 97.6 D) ) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 83) A mathematics professor gives two different tests to two sections of his college algebra courses. The first class has a mean of 56 with a standard deviation of 9 while the second class has a mean of 75 with a standard deviation of 15. A student from the first class scores a 62 on the test while a student from the second class scores an 83 on the test. Compare the scores. 83) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 84) Compare the scores: a score of 75 on a test with a mean of 65 and a standard deviation of 8 and a score of 75 on a test with a mean of 70 and a standard deviation of 4. A) A score of 75 with a mean of 70 and a standard deviation of 4 is better. B) The two scores are statistically the same. C) You cannot determine which score is better from the given information. D) A score of 75 with a mean of 65 and a standard deviation of 8 is better. 84) 85) Compare the scores: a score of 88 on a test with a mean of 79 and a score of 78 on a test with a mean of 70. A) You cannot determine which score is better from the given information. B) The two scores are statistically the same. C) A score of 75 with a mean of 70 and a standard deviation of 4 is better. D) A score of 75 with a mean of 65 and a standard deviation of 8 is better. 85) 86) Compare the scores: a score of 220 on a test with a mean of 200 and a standard deviation of 21 and a score of 90 on a test with a mean of 80 and a standard deviation of 8. A) You cannot determine which score is better from the given information. B) A score of 220 with a mean of 200 and a standard deviation of 21 is better. C) The two scores are statistically the same. D) A score of 90 with a mean of 80 and a standard deviation of 8 is better. 86) 10

11 87) Two high school students took equivalent language tests, one in German and one in French. The student taking the German test, for which the mean was 66 and the standard deviation was 8, scored an 82, while the student taking the French test, for which the mean was 27 and the standard deviation was 5, scored a 35. Compare the scores. A) A score of 35 with a mean of 27 and a standard deviation of 5 is better. B) The two scores are statistically the same. C) A score of 82 with a mean of 66 and a standard deviation of 8 is better. D) You cannot determine which score is better from the given information. 87) 88) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 1130 on the SAT and 25 on the ACT. Compare the scores. A) You cannot determine which score is better from the given information. B) The two scores are statistically the same. C) A score of 1130 on the SAT test was better. D) A score of 25 on the ACT test was better. 88) 89) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the SAT and 16 on the ACT. Compare the scores. A) A score of 860 on the SAT test was better. B) You cannot determine which score is better from the given information. C) A score of 16 on the ACT test was better. D) The two scores are statistically the same. 89) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 90) Assume that blood pressure readings are normally distributed with μ= 111 and σ = 7. A researcher wishes to select people for a study but wants to exclude the top and bottom 10 percent. What would be the upper and lower readings to qualify people to participate in the study? 90) 91) Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $4000. What is the cutoff salary for teachers in the top 10%? 91) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 92) Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $28,000 and a standard deviation of $3000. What is the cutoff salary for teachers in the bottom 10%? A) $23,065 B) $32,935 C) $31,840 D) $24,160 92) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 93) The times for completing one circuit of a bicycle course are normally distributed with a mean of 64.5 minutes and a standard deviation of 7.8 minutes. An association wants to sponsor a race but will cut the bottom 25% of riders. In a trial run, what should be the cutoff time? 93) 11

12 94) Assume that the heights of men are normally distributed with a mean of 70.6 inches and a standard deviation of 2.2 inches. If the top 5 percent and bottom 5 percent are excluded for an experiment, what are the cutoff heights to be eligible for this experiment? Round your answers to one decimal place. 94) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 95) Assume that the heights of women are normally distributed with a mean of 63.5 inches and a standard deviation of 2.5 inches. Find Q3, the third quartile that separates the bottom 75% from the top 25%. A) 61.8 B) 66.4 C) 66.7 D) ) 96) The body temperatures of adults are normally distributed with a mean of 98.6 F and a standard deviation of 0.19 F. What temperature represents the 95th percentile? A) F B) F C) F D) F 96) 97) In a certain normal distribution, find the standard deviation σ when μ = 50 and 10.56% of the area lies to the right of 55. A) 5 B) 4 C) 3 D) 2 97) 98) In a certain normal distribution, find the mean μ when σ = 5 and 5.48% of the area lies to the left of 78. A) 94 B) 70 C) 86 D) 62 98) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 99) In a certain normal distribution, 6.3% of the area lies to the left of 36 and 6.3% of the area lies to the right of 42. Find the mean μ and the standard deviation σ. 99) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 100) A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 48,400 miles and a standard deviation of 5000 miles. If the manufacturer is willing to replace no more than 10% of the tires, what should be the approximate number of miles for a warranty? A) 42,000 B) 40,175 C) 56,625 D) 54, ) 12

13 Answer Key Testname: MATH211_NORMAL_DISTR 1) B 2) C 3) C 4) C 5) C 6) B 7) C 8) D 9) C 10) D 11) A 12) C 13) D 14) D 15) A 16) A 17) D 18) C 19) C 20) B 21) C 22) A 23) A 24) C 25) D 26) C 27) B 28) A 29) D 30) B 31) B 32) C 33) C 34) A 35) A 36) D 37) B 38) B 39) C 40) A 41) D 42) C 43) A 44) A 45) C 46) B 47) B 48) A 49) A 50) C 13

14 Answer Key Testname: MATH211_NORMAL_DISTR 51) B 52) B 53) A 54) B 55) D 56) D 57) A 58) B 59) A 60) A 61) B 62) A 63) If x = 58, then z = and P(x) = If x = 80, then z = 6.56 and P(x) = P(58 < x < 80) = = ) About 6 pregnancies 65) About 3 teenage boys 66) About 43 weeks 67) About 197 women 68) About 19 men 69) z = ) z = ) z = ) z = ) B 74) D 75) C 76) C 77) C 78) A 79) A 80) A 81) C 82) C 83) z = (62-56)/9 = 0.667; z = (83-75)/15 = The student with the score of 62 has the better score. 84) B 85) A 86) D 87) C 88) D 89) A 90) (102.0, 120.0) 91) x = μ + zσ = 32,000 + (1.28)(4000) = $37,120 92) D 93) x = μ + zσ = (0.675)(7.8) = ) 67.0 inches, 74.2 inches 95) D 96) B 97) B 98) C 99) μ = 39, σ =

15 Answer Key Testname: MATH211_NORMAL_DISTR 100) A 15