Question

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .3 inches. What is the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long?

Answer 1

Answer:

0.3707

Step-by-step explanation:

Mean length = 30.05 inches

Standard deviation = 0.3 inches

We are supposed to find the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long

Formula : $Z=\frac{x-\mu}{\sigma}$

$\mu = 30.05\\\sigma = 0.3$

x= 29.95

Substitute the values :

$Z=\frac{29.95-30.05}{0.3}$

$Z=-0.33$

Refer the z table for p value

p value = 0.3707

So, the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long is 0.3707