Question

A normal population has a mean of 21 and a standard deviation of 5.

a. Compute the Z value associated with 25 (round answer to 2 decimal places)

b. What proportion of the population is between 21 and 25? (Round z-score computation to 2 decimal places and final answer to 4 decimal places)

c. What proportion of the population is less than 17? (Round z-score computation to 2 decimal places and final answer to 4 decimal places)

Answer 1

Solution :

Given that ,

mean = = 21

standard deviation =  = 5

a) x = 25

Using z-score formula,

z = x - /   

z = 25 - 21 / 5

z = 0.80

b) P( 21 < x < 25) = P[(21 - 21)/ 5) < (x - ) /  < (25 - 21) / 5) ]

= P(0 < z < 0.80)

= P(z < 0.80) - P(z < 0)

Using z table,

= 0.7881 - 0.5

= 0.2881

c) P(x < 17) = P[(x - ) / < (17 - 21) / 5 ]

= P(z < -0.80)

Using z table,

= 0.2119