Question

Smalltown Elevator produces elevator rails. To meet specifications, an elevator rail must be between 0.995 inches and 1.005 inches in diameter. Suppose that the diameter of an elevator rail follows a normal random variable with mean of 1 inch and standard deviation of 0.003 inches. Rounded to the nearest one tenth of one percent, what fraction of all elevator rails will meet specifications?

Answer 1

Answer: 90.5%

Explanation:

Given: Mean :
`\mu = 1\text{ inch}`

Standard deviation :
`\sigma = 0.003\text{ inch}`

The formula to calculate z is given by :-

`z=(x-\mu)/(\sigma)`

For x= 0.995

`z=(0.995-1)/(0.003)=-1.66666666667\approx-1.67`

The P Value =
`P(z<-1.67)=0.0474597`

For x= 1.005

`z=(1.005-1)/(0.003)=1.66666666667\approx1.67`

The P Value =
`P(z<1.67)= 0.9525403`

`\text{Now, }P(0.995<X<1.005)=P(X<1.005)-P(X<0.995)\\\\=P(z<1.67)-P(z<-1.67)\\\\=0.9525403-0.0474597=0.9050806`

In percent ,

`P(0.995<X<1.005)=0.9050806*100=90.50806\%\approx90.5\%`