Question

Given a normal distribution, X, with mean, 135, and standard deviation, sigma = 40.

Fill the blank space.
A. What is the X value with Z-score equal to z = -2.39? __________
B. What is the probability of X is less than or equal to 45.3? _________ %

Answer 1

Part a)

X = µ + Z σ

X = 135 + ( - 2.39 ) * 40

X = 39.4

Part b)

X ~ N ( µ = 135 , σ = 40 )
P ( X <= 45.3 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 45.3 - 135 ) / 40
Z = -2.2425
P ( ( X - µ ) / σ ) < ( 45.3 - 135 ) / 40 )
P ( X <= 45.3 ) = P ( Z < -2.2425 )
P ( X <= 45.3 ) = 0.0125