Question

A population is normally distributed with mean μ = 100 and standard deviation σ = 20. Find the probability that a value randomly selected from this population will have a value between 90 and 130. (i.e., calculate P(90<X<130))

Answer 1

Solution :

Given that ,

mean = = 100

standard deviation = = 20

P(90< x < 130) = P[(90-100) /20 < (x - ) / < (130 -100) / 20)]

= P( -0.5< Z < 1.5)

= P(Z <1.5 ) - P(Z <-0.5 )

Using z table   

= 0.9332-0.3085

probability= 0.6247