Question

A random variable is normally distributed with a mean of

μ = 60

and a standard deviation of

σ = 5.

What is the probability the random variable will assume a value between 45 and 75? (Round your answer to three decimal places.)

Answer 1

Solution:

Given that,

mean =  = 60

standard deviation = = 5

P ( 45 < x < 75 )

= P ( 45 - 60 / 5) < ( x -  / ) < ( 75 - 60 / 5)

= P ( - 15 / 5 < z < 15 / 15 )

= P (- 3 < z < 3 )

= P (z < 3 ) - p ( z < - 3 )

Using z table

= 0.9987 - 0.0013

= 0.9974

Probability = 0.997