ch.6 Statistics
29. A normal distribution has μ = 20 and σ = 4. What is the probability of randomly selecting a score greater than 25 from this distribution? a. 0.3944 c. 0.8944 b. 0.1056 d. 0.7888
b
28. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score less than X = 130 is p = 0.9987.
f
4. For a normal distribution, proportions in the right-hand tail are positive, and proportions in the left-hand tail are negative.
f
2. A class consists of 10 male and 30 female students. If one student is randomly selected from the class, what is the probability of selecting a male student? a. 10/30 c. 1/10 b. 10/40 d. 1/40
b
45. A normal distribution has a mean of µ = 24 with σ = 3. What is the minimum score needed to be in the top 14% of the distribution?
c
20. For a normal distribution, the z-score boundary that separates the highest 2.5% of the scores from the rest is z = -1.96.
f
21. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score greater than X = 110 is p = 0.6915.
f
25. For a normal distribution with µ = 50 and σ = 10, the line separating the highest 10% of the scores from the rest is located at X = 51.28.
f
20. What is the probability of randomly selecting a z-score greater than z = 0.75 from a normal distribution? a. 0.7734 c. 0.2734 b. 0.2266 d. 0.4532
b
1. All probabilities can be expressed as decimal values ranging from 0 to 1.00.
t
11. A vertical line drawn through a normal distribution at z = -0.50 separates the distribution into two sections. The proportion in the larger section is 0.6915.
t
19. A vertical line is drawn through a normal distribution so that 47.5% of the distribution is located between the line and the mean. The line is drawn at z = 1.96 or at z = -1.96.
t
22. For a population with a mean of μ = 80 and σ = 10, only 2.28% of the scores are greater than X = 100.
t
26. For a normal distribution with µ = 80 and σ = 10, the score that separates the bottom 10% of the distribution from the rest is 67.2
t
27. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score less than X = 95 is p = 0.4013.
t
14. A vertical line drawn through a normal distribution at z = -1.00 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the tail? a. 0.8413 c. 0.3413 b. 0.1587 d. -0.8413
b
10. What proportion of a normal distribution is located between the mean and z = -1.40? a. 0.0808 c. -0.0808 b. 0.4192 d. -0.4192
b
29. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score between X = 90 and X = 100 is p = 0.3085.
f
30. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score between X = 80 and X = 120 is p = 0.3413.
f
21. What is the probability of randomly selecting a z-score less than z = 1.25 from a normal distribution? a. 0.8944 c. 0.3944 b. 0.1056 d. 0.2112
a
28. A normal distribution has a mean of µ = 40 with σ = 10. If a vertical line is drawn through the distribution at X = 35, what proportion of the scores are on the left side of the line? a. 0.3085 c. 0.0668 b. 0.6915 d. 0.9332
a
9. What proportion of a normal distribution is located between the mean and z = 1.40? a. 0.9192 c. 0.4192 b. 0.0808 d. 0.8384
c
11. A vertical line drawn through a normal distribution at z = 0.50 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the body? a. 0.6915 c. 0.1915 b. 0.3085 d. 0.3830
a
13. A vertical line drawn through a normal distribution at z = -1.00 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the body? a. 0.8413 c. 0.3413 b. 0.1587 d. -0.1587
a
36. A normal distribution has a mean of µ = 40 with σ = 8. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 34? a. 0.7734 c. 0.2734 b. 0.2266 d. 0.4532
b
42. A normal distribution has a mean of µ = 80 with σ = 20. What score separates the highest 15% of the distribution from the rest of the scores? a. X = 59.2 c. X = 95 b. X = 100.8 d. X = 65
b
43. A normal distribution has a mean of µ = 80 with σ = 20. What score separates the highest 40% of the distribution from the rest of the scores? a. X = 75 c. X = 54.4 b. X = 85 d. X = 105.6
b
44. A normal distribution has a mean of µ = 80 with σ = 20. What score separates the lowest 30% of the distribution from the rest of the scores? a. X = 90.4 c. X = 110 b. X = 69.6 d. X = 50
b
7. What proportion of a normal distribution is located in the tail beyond z = 1.50? a. 0.9332 c. 0.4332 b. 0.0668 d. 0.1336
b
8. What proportion of a normal distribution is located in the tail beyond z = -1.00? a. 0.8413 c. -0.3413 b. 0.1587 d. -0.1587
b
19. What proportion of a normal distribution is located between z = 0 and z = +1.50? a. 0.9332 c. 0.4332 b. 0.0668 d. 0.8664
c
25. What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%? a. z = 0.52 c. z = -0.52 b. z = 0.84 d. z = -0.84
c
27. A normal distribution has a mean of µ = 40 with σ = 10. If a vertical line is drawn through the distribution at X = 55, what proportion of the scores are on the right side of the line? a. 0.3085 c. 0.0668 b. 0.6915 d. 0.9332
c
3. A class consists of 10 male and 30 female students. A random sample of n = 3 students is selected. If the first two students are both females, what is the probability that the third student is a male? a. 10/37 c. 10/40 b. 10/38 d. 8/38
c
1. Which of the following is a requirement for a random sample? a. Every individual has an equal chance of being selected. b. The probabilities cannot change during a series of selections. c. There must be sampling with replacement. d. All of the other 3 choices are correct.
d
17. What proportion of a normal distribution is located between z = -1.25 and z = +1.25? a. 0.8944 c. 0.3944 b. 0.2112 d. 0.7888
d
18. What proportion of a normal distribution is located between z = -1.50 and z = +1.50? a. 0.9332 c. 0.4332 b. 0.0668 d. 0.8664
d
26. What z-score values form the boundaries for the middle 60% of a normal distribution? a. z = +0.25 and z = -0.25 c. z = +0.52 and z = -0.52 b. z = +0.39 and z = -0.39 d. z = +0.84 and z = -0.84
d
33. A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 84? a. 0.7881 c. 0.2881 b. 0.5762 d. 0.2119
d
40. A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 90 and X = 110? a. 0.6915 c. 0.1915 b. 0.3085 d. 0.3830
d
47. John drives to work each morning, and the trip takes an average of µ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John's drive to work will take less than 35 minutes? a. 0.6554 c. 0.7257 b. 0.3446 d. 0.2743
d
48. John drives to work each morning, and the trip takes an average of µ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John's drive to work will take between 36 and 40 minutes? a. 0.0793 c. 0.1554 b. 0.1526 d. 0.3108
d
49. IQ scores form a normal distribution with µ = 100 and σ = 15. Individuals with IQs above 140 are classified in the genius category. What proportion of the population consists of geniuses? a. 0.9962 c. 0.4962 b. 0.5038 d. 0.0038
d
6. Which of the following accurately describes the proportions in the body of a normal distribution? a. Body proportions on the right side of the z-score are greater than 0.50; on the left side, they are less than 0.50. b. Body proportions on the right side of the z-score are less than 0.50; on the left side, they are greater than 0.50. c. Body proportions on either side of the z-score are less than 0.50. d. Body proportions on either side of the z-score are greater than 0.50.
d
7. When the z-score value in a normal distribution is negative, the body is on the right-hand side of the distribution.
t
31. A normal distribution has a mean of µ = 60 with σ = 8. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 54? a. 0.7734 c. 0.2734 b. 0.2266 d. 0.3085
a
13. For a normal distribution, the proportion in the tail beyond z = -2.00 is equal to -0.0228.
f
12. For any normal distribution, the proportion in the tail beyond z = 2.00 is p = 0.0228.
t
22. What is the probability of randomly selecting a z-score greater than z = -0.75 from a normal distribution? a. 0.7734 c. 0.2734 b. 0.2266 d. 0.4532
a
15. For a normal distribution, the proportion in the tail beyond z = 0.30 is p = 0.1179.
f
34. A normal distribution has a mean of µ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 58? a. 0.8413 c. 0.3413 b. 0.1577 d. 0.6826
a
16. A vertical line is drawn through a normal distribution at z = 1.20. What proportion of the distribution is on the left-hand side of the line? a. 0.8849 c. 0.3849 b. 0.1151 d. 0.7698
a
24. What z-score value separates the highest 10% of the scores in a normal distribution from the lowest 90%? a. z = 1.28 c. z = -1.28 b. z = 0.25 d. z = -0.25
a
46. Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted? a. X = 475 c. X = 440 b. X = 525 d. X = 560
a
12. A vertical line drawn through a normal distribution at z = 0.50 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the tail? a. 0.6915 c. 0.1915 b. 0.3085 d. 0.3830
b
15. A vertical line is drawn through a normal distribution at z = 0.80. What proportion of the distribution is on the right-hand side of the line? a. 0.7881 c. 0.2881 b. 0.2119 d. 0.5762
b
23. What is the probability of randomly selecting a z-score less than z = -1.25 from a normal distribution? a. 0.8944 c. 0.3944 b. 0.1056 d. 0.2112
b
30. A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting a score greater than 90 from this distribution? a. 0.8413 c. 0.3085 b. 0.1587 d. 0.6915
b
32. A normal distribution has a mean of µ = 70 with σ = 10. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 82? a. 0.7698 c. 0.1151 b. 0.3849 d. 0.8849
c
35. A normal distribution has a mean of µ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 76? a. 0.1915 c. 0.6915 b. 0.3085 d. 0.3830
c
37. A normal distribution has a mean of µ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 55? a. 0.3944 c. 0.8944 b. 0.1056 d. 0.7888
c
38. A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 80 and X = 100? a. 0.8413 c. 0.3413 b. 0.1587 d. 0.6826
c
39. A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 100 and X = 130? a. 0.9332 c. 0.4332 b. 0.0668 d. 0.8664
c
4. Which of the following accurately describes the proportions in the tails of a normal distribution? a. Proportions in the right-hand tail are positive, and proportions in the left-hand tail are negative. b. Proportions in the right-hand tail are negative, and proportions in the left-hand tail are positive. c. Proportions in both tails are positive. d. Proportions in both tails are negative.
c
41. A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 90 and X = 120? a. 0.1498 c. 0.5328 b. 0.4672 d. 0.2996
c
5. Which of the following accurately describes the proportions in the tails of a normal distribution? a. Proportions in the right-hand tail are greater than 0.50, and proportions in the left-hand tail are less than 0.50. b. Proportions in the right-hand tail are less than 0.50, and proportions in the left-hand tail are greater than 0.50. c. Proportions in both tails are less than 0.50. d. Proportions in both tails are greater than 0.50.
c
50. IQ scores form a normal distribution with µ = 100 and σ = 15. Individuals with IQs between 90 and110 are classified as average. What proportion of the population is average? a. 0.7486 c. 0.4972 b. 0.5028 d. 0.2486
c
10. A vertical line drawn through a normal distribution at z = -0.75 separates the distribution into two sections. The proportion in the smaller section is 0.2734.
f
16. For a normal distribution, the proportion located between z = -1.00 and z = +1.00 is p = 34.13%
f
2. The probability of randomly selecting a red marble from a jar that contains 10 red marbles and 20 blue marbles is 1/30.
f
23. For a normal distribution with µ = 100 and σ = 20, the score that separates the top 60% of the distribution from the bottom 40% is X = 105.
f
24. The middle 90% of a normal distribution is located between z = -1.96 and z = 1.96
f
3. A jar contains 10 red marbles and 20 blue marbles. If you take a random sample of two marbles from this jar, and the first marble is blue, then the probability that the second marble is blue is p = 19/29.
f
14. For any normal distribution, exactly 97.50% of the z-score values are less than z = 1.96.
t
17. For any normal distribution, the probability of randomly selecting a z-score less than z = 1.40 is p = 0.9192.
t
18. A vertical line is drawn through a normal distribution so that the proportion in the tail is 0.1841. The line was drawn at z = 0.90 or at z = -0.90.
t
5. The proportion in the tail of a normal distribution can never be more than 0.50.
t
6. The proportion in the body of a normal distribution can never be less than 0.50.
t
8. The tail is on the right side of a normal distribution for any z-score value greater than zero.
t
9. A vertical line drawn through a normal distribution at z = 1.40 divides the distribution into two sections. The proportion in the smaller section is 0.0808.
t
