Normal Distribution and Z Score

Adam's Z-score on a test is +2.50. What does this mean?

• Adam's score has a 2.5% chance of being better than any other randomly selected score.

• Adam's test score was better than 25% of his peers.

• He scored 2.5 standard deviations above the average.

• He did terrible.

Test has a mean of 40 and a standard deviation of 10. What is the percent of people that scored above 62?

• 1.39%

• 45.34%

• 98.41%

• 22.34%

What is the standard deviation of the distribution?

• 1010

• 20

• 60

• √20

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

•  28,000 km and 32,000 km.

• 24,000 km and 34,000 km.

• 26,000 km and 34,000 km.

• 27,000 km and 31,000 km.

The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. Between what heights do the middle 95% of men fall? 

• 66.5-71.5

• 64-74

• 61.5-76.5

• 65-73

The normal curve is symmetrical about the mean.

• True

• False

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%

What will be the miles per gallon for a Toyota Camry when the average mpg is 23, it has a z value of 1.5 and a standard deviation of 2?

• 25

• 20

• 26

• 68

Pat and Tom took a test with mean 80 and SD 9. Pat scored a 76; Tom scored a 94. Find the percent of people between their scores.

• 68.78%

• 63.29%

• 61.06%

• 34.25%

Test has a mean of 40, standard deviation of 10. What is the percent of people with a score below 37?

• 52.97%

• 31.53%

• 48.99%

• 38.21%