Question

A manufacturer knows that their items have a normally distributed length, with a mean of 14 inches, andstandard deviation of 0.6 inches.If one item is chosen at random, what is the probability that it is less than 12.7 inches long? Round to at least 4decimal places.

Answer 1

Given the information on the problem, we can use the mean and the standard deviation to find the z score:

`\begin{gathered} \mu=14 \\ \sigma=0.6 \\ \Rightarrow z=(12.7-14)/(0.6)=-2.16 \end{gathered}`

thus, we have that the probability that the item will be less than 12.7 inches long is:

`P(Z<-2.16)=0.0154`

according to the z-score chart.

Therefore, 1.54% will be shorter than 12.7 inches