Question

A random variable is normally distributed with a mean of μ = 70 and a standard deviation of σ = 10

What is the probability the random variable will assume a value between 50 and 90? (Round your answer to three decimal places.)

What is the probability the random variable will assume a value between 60 and 80? (Round your answer to three decimal places.)

Answer 1

Solution :

Given that,

mean = = 70

standard deviation = =10

a ) P ( 50 < x < 90 )

P ( 50 - 70 / 10) < ( x -  / ) < ( 90 - 70 / 10 )

P ( - 20 / 10 < z < 20 / 10 )

P (- 2 < z < 2 )

P (z < 2 ) - p ( z < - 2 )

Using z table

= 0.9772 - 0.0228

= 0.9544

Probability = 0.954

b ) P ( 60 < x < 80 )

P ( 60 - 70 / 10) < ( x -  / ) < ( 80 - 70 / 10 )

P ( - 10 / 10 < z < 10 / 10 )

P (- 1 < z < 1 )

P (z < 1 ) - p ( z < - 1 )

Using z table

= 0.8413 - 0.1587

= 0.6826

Probability = 0.683