Question

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

a. Compute the z value associated with 27. (Round your answer to 2 decimal places.)

b. 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.)

Answer 1

Solution :

Given that ,

mean = = 21

standard deviation = = 3

a.

using z score formula

z= (x - ) / =27-21/3=2

z=2

b.

P(21< x < 27) = P[(21 - 21) / 3< (x - ) / < (27 - 21) /3 )]

= P(0 < Z < 2)

= P(Z <2 ) - P(Z < 0)

Using z table   

= 0.9772 - 0.5

=0.4772