Question

A normal population has a mean of 20.0 and a standard deviation of 4.0.

a). Compute the z value associated with 25.0. (Round your answer to 2 decimal places.)

b). What proportion of the population is between 20.0 and 25.0? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

c). What proportion of the population is less than 18.0? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Answer 1

Solution :

Given that ,

mean = = 20

standard deviation = = 4

(a)

x = 25

z = (x - ) / = (25 - 20) / 4 = 5 / 4 = 1.25

z value = 1.25

(b)

P(20 < x < 25) = P((20 - 20) / 4) < (x - ) /  < (25 - 20) / 4) )

= P(0 < z < 1.25)

= P(z < 1.25) - P(z < 0)

= 0.8944 - 0.5

= 0.3944

Proportion = 0.3944

(c)

P(x < 18) = P((x - ) / < (18 - 20) / 4)

= P(z < -0.5)

= 0.3085

Proportion = 0.3085