Calculations Shown

1. The amount of Jen’s monthly electric bill is normally distributed with a mean of $160 and a standard deviation of $14. Fill in the blanks. 95% of her electric bills are between __________ and __________. Apply the 68-95-99.7 rule to this question.

A. $140, $190

B. $132, $190

C. $140, $188

D. $132, $188

2. The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 460 pencils, approximately how many would you expect to have a diameter less than 0.293 inches?

A. 123

B. 118

C. 112

D. 111

3. The amount of Jen’s monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.

A. About $46.30

B. About $43.30

C. About $43.40

D. About $43.20

4. The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 6. If 9 fish are randomly selected, what is the likelihood that the mean weight will be between 17.6 and 21.6 lb?

A. 0.9370

B. 0.6800

C. 0.6730

D. 0.0968

5. A math teacher gives two different tests to measure students’ aptitude for math. Scores on the first test are normally distributed with a mean of 24 and a standard deviation of 4.5. Scores on the second test are normally distributed with a mean of 70 and a standard deviation of 11.3. Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.)

A. 87

B. 85

C. 86

D. 83

6. If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?

A. About 84%

B. About 68%

C. About 32%

D. About 16%

7. The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks. In 95% of the years, the precipitation in this city is between __________ and __________ inches. Apply the 68-95-99.7 rule to this question.

A. 21.2, 34.8

B. 21.2, 34.6

C. 22.4, 34.6

D. 22.4, 34.8

8. A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?

A. 19.46%

B. 12.85%

C. 2.87%

D. 13.46%

9. The scores on a certain test are normally distributed with a mean score of 58 and a standard deviation of 4. What is the likelihood that a sample of 90 students will have a mean score of at least 58.4216?

A. 0.8413

B. 0.3413

C. 0.3174

D. 0.1587

10. If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

A. About 25%

B. About 50%

C. About 75%

D. About 68%

11. Which of the following statements concerning the standard normal curve is/are true (if any)?

a) The area under the standard normal curve to the left of -3 is zero.

b) The area under the standard normal curve between any two z-scores is greater than zero.

c) The area under the standard normal curve between two z-scores will be negative if both z-scores are negative.

d) The area under the standard normal curve to the left of any z-score is less than 1.

A. a, b

B. b, d

C. a, c

D. a

12. At one college, GPA’s are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.

A. 3.53

B. 3.42

C. 3.23

D. 3.13