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=(x-\mu)/(\sigma)`

Using this formula in our problem, we have:

`z=(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`