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

Answer:

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

Step-by-step 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:$Z= \frac{x-\mu}{\sigma}$

At x = 600

$Z= \frac{600-600}{100}$

Z=0

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

At x = 700

$Z= \frac{700-600}{100}$

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