A normal population has a mean of 200 and a standard deviati

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

a. 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.)

b. 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.)

Solution

Let X be the variable

X is N(20, 4)

a) P(20<x<25)

= P(0<z<5/4)

= P(0<z<1.25) =

0.3944

b) P(X<18)

= P(Z<-0.5)

= 0.5-0.1915

= 0.3085