Question

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches. A sample of 36 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 29.82 and 30.27 inches long?

Answer 1

Answer: 0.8490

Step-by-step explanation:

Given :  The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches.

i.e. $\mu=30$ and $\sigma=0.9$

Let x denotes the lengths of aluminum-coated steel sheets.

Required Formula : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For n= 36 , the probability that the average length of a sheet is between 29.82 and 30.27 inches long will be :-

$P(29.82$

∴ Required probability = 0.8490