Question

A normal population has a mean of 21 and a standard deviation of 3. Use Appendix B.3.

Compute the z value associated with 27. (Round your answer to 2 decimal places.) What proportion of the population is between 21 and 27? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

What proportion of the population is less than 18? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Answer 1

Normal population has mean = 21 and standard deviation = 3

The formula to find the z score associated with x = 27 is

Proportion between 21 and 27

The z score corresponding to 27 is 2, now the z score for x = 21 is

Using z table, Appendix B3, the probability for z = 0 is 0.5000 and the probability for z = 2 is 0.9772

To find the between proportion, just subtract small from large that is 0.9772 - 0.5000 = 0.4772

The proportion of the population between 21 and 27 is 0.4772

Proportion less than 18

First find z score for 18

The probability for z = -1 is 0.1587, the table provides the less than proportion.

The proportion of the population less than 18 is 0.1587