Question

Given X with a normal distribution with mean 39.5 and standard deviation 5.0.

a. What is the probability that X is between 38.0 and 42.5?

b. What value of X falls at the 85^th percentile?

Answer 1

solution'

given that

(A)P(38.0< x <42.5 ) = P[(38.0-39.5) /5.0 < (x - ) / < (42.5-39.5) /5.0 )]

= P(-0.3 < Z <0.6 )

= P(Z <0.6 ) - P(Z <-0.3 )

Using z table   

=  0.7257-0.3821

probability=0.3436

(B)

Using standard normal table,

P(Z < z) =85 %

= P(Z < z) = 0.85  

= P(Z <1.04 ) = 0.85

z = 1.04 Using standard normal z table,

Using z-score formula  

x= z * +

x= 1.04 *5.0+39.5

x= 44.7

x=45