Question

A manufacturer knows that their items have a normally distributed length, with a mean of 18.2 inches, and standard deviation of 4.8 inches one is chosen at random , what is the probability that it is less than 28.6 inches long?

Answer 1

To find the corresponding probability, first we need to convert our value to a z-score using the following formula:

$z=\frac{x-\mu}{\sigma}$

Using this formula in our problem, we have:

$z=\frac{28.6-18.2}{4.8}\approx2.08$

Then, checking the corresponding probability in a z-table, we have:

$P(z\leq2.08)=0.9812$