Normal Distribution and Probability

For a certain type of computer, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours.

• 0.9082

• 0.8989

• 0.5000

• 0.4087

Find the Z-score.

Mean = 22

Standard Deviation: 3.1

x = 29

• 2.26

• 16.45

• -2.26

• 1.26

Find the Z-score.

Mean = 21

Standard Deviation: 1.3

x = 22

• 0.77

• 5.33

• 1.07

• 1.26

If heights of 3rd graders follow a normal distribution with a mean of 52 inches and a standard deviation of 2.5 inches, what is the z score of a 3rd grader who is 47 inches tall?

• -5

• -2

• 2

• 5

• 298

• 296

• 220

• 380

A national achievement test is administered annually to 3rd graders. The test has a mean score of 80 and a standard deviation of 8. If Jane's z-score is (-1.2), what was her score on the test?

• 88

• 72

• 89.6

• 70.4

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

• 68%

• 34%

• 16%

• 2.5%

For a randomly selected subject in a standard normal distribution (mean is 0 and standard deviation is 1), find the probability of a score between 1.37 and 2.42.

• 0.078

• 0.785

• 0.223

• 0.023

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find the score which separates the lower 60% from the top 40%.

•  187.5

• 212.7

• 207.8

•  211.3

The speeds of cars on the highway have a mean of 95 km/h with a standard deviation of 5 km/h. What percentage of cars averaged less than 85 km/h?

• .15%

• 2.35%

• 2.5%

• 18.5%