Question

PVC pipe is manufactured with mean diameter of 1.01 inch and a standard deviation of 0.003 inch. Find the probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 inch and less than 1.012 inch.

Answer 1

Answer: 0.8186

Explanation:

Given: Mean :
`\mu=1.01\text{ inch}`

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

Sample size :
`n=9`

The formula to calculate z-score :-

`z=(X-\mu)/((\sigma)/(√(n)))`

For x=1.009 inch

`z=(1.009-1.01)/((0.003)/(√(9)))=-1`

For x=1.012 inch

`z=(1.012-1.01)/((0.003)/(√(9)))=2`

Now, The p-value =
`P(-1<z<2)=P(2)-P(-1)=0.9772498-0.1586553=0.8185945\approx0.8186`

Hence, the required probability = 0.8186