Question

The playing life of a Sunshine radio is normally distributed with mean LaTeX: \muμ = 600 hours and standard deviation LaTeX: \sigmaσ = 100 hours. What is the probability that a radio selected at random will last from 600 to 700 hours

Answer 1

The probability that a radio selected at random will last from 600 to 700 hours is 0.3413

Explanation:

The playing life of a Sunshine radio is normally distributed

Mean =
`\mu = 600 hours`

Standard deviation =
`\sigma = 100 hours`

We are supposed to find the probability that a radio selected at random will last from 600 to 700 hours i.e.P(600<x<700)

Formula:
`Z= (x-\mu)/(\sigma)`

At x = 600

`Z= (600-600)/(100)`

Z=0

`P(X<600)=P(z<0)=0.5`

At x = 700

`Z= (700-600)/(100)`

Z=1

`P(X<700)=P(z<1)=0.8413`

`P(600<x<700)=P(x<700)-P(x<600)=0.8413-0.5=0.3413`

Hence the probability that a radio selected at random will last from 600 to 700 hours is 0.3413