Question

Suppose X has a normal distribution with mean 115 and variance 25. Find the 67th percentile of the distribution of X.

A. 134.8

B. 117.2

C.136

D.131.425

Answer 1

solution

Given that,

mean = = 115

standard deviation = =25=5

Using standard normal table,

P(Z < z) =67 %

= P(Z < z) = 0.67  

= P(Z < 0.44) = 0.67

z = 0.44 Using standard normal z table,

Using z-score formula  

x= z * +

x= 0.44 *5+115

x= 117.2