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

Step-by-step 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 :-

$z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x=1.009 inch

$z=\dfrac{1.009-1.01}{\dfrac{0.003}{\sqrt{9}}}=-1$

For x=1.012 inch

$z=\dfrac{1.012-1.01}{\dfrac{0.003}{\sqrt{9}}}=2$

Now, The p-value =$P(-1$

Hence, the required probability = 0.8186