Question

Given a normal distribution, X, with mean, 150, and standard deviation, sigma = 42.

A. What is the X value with Z-score equal to z = 2.77?

B. What is the probability of X is less than or equal to 266.3? %

Answer 1

solution

(A)Using z-score formula  

x= z * +

x= 2.77 *42+150

x= 266.34

(B)

P(x  266.3)

= P[(x - ) /   (266.3-150) / 42]

= P(z 2.77)

Using z table,

=0.9972

probability=0.9972