Question

Suppose that X is normally distributed with mean 85 and standard deviation 24.

A. What is the probability that X is greater than 115.24?

Probability =

B. What value of X does only the top 19% exceed?

X =

Answer 1

Solution :

Given that,

mean = = 85

standard deviation = =24

A ) P (x > 115.24 )

= 1 - P (x < 115.24 )

= 1 - P ( x -  / ) < ( 115.24 - 85 / 24)

= 1 - P ( z < 30.24 / 24 )

= 1 - P ( z < 1.26 )

Using z table

= 1 - 0.8962

= 0.1038

Probability = 0.1038

B ) P(Z > z) = 19%

1 - P(Z < z) = 0.19

P(Z < z) = 1 - 0.19 = 0.81

Using standard normal table,

P(Z < 0.8779) = 0.81

z = 0.88

Using z-score formula,

x = z * +

x = 0.88 * 24 + 85 = 106.12

X = 106.12