Normal Distribution with Z Score

The ages of the population of people living in Meru area in Ipoh are Normally distributed with mean 43 and standard deviation 14

The town has a population of 5,000.

How many would you expect to be aged between 22 and 57?

You can use this Standard Normal Distribution curve:

• 1750

• 3860

• 3870

• 4330

68% of the marks in a test are between 51 and 64

Assuming this data is normally distributed, what are the mean and standard deviation?

• Mean = 57

  S.D. = 6.5

• Mean = 57

  S.D. = 7

• Mean = 57.5

  S.D. = 6.5

• Mean = 57.5

  S.D. = 13

Find the Z-score.

Mean = 22

Standard Deviation: 3.1

x = 29

• 2.26

• 16.45

• -2.26

• 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

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.

Which of the following is a formula that describes calculating a z-score?

• Z = (score - mean) / stand. devation

• Z = (mean - score) / stand. dev.

• Z = score/stand. dev/ mean

• Z = dragonball

The sign of the z-score indicates whether the location is above(positive) or below(negative) the mean.

• True

• False

What is the Z-score for Paula if she got 1400 on the SAT, the mean was 1100 and the standard deviation was 275?

• -1.90

• -1.09

• +1.09

• +1.90

Find the mean.

Z-score = -1.4

Standard Deviation: 7

x = 20

• 29.8

• 10.2

• -21

• 35

Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. What score would you need to fall at the 84th percentile?

• 84

• 400

• 500

• 600