Question

Forearm lengths of men, measured from the elbow to the middle fingertip, are normallydistributed with a mean 18.8 inches and a standard deviation 1.1 inches.If 1 man is randomly selected, what is the probability that his forearm length is below 17

Answer 1

Solution

Part A

What are the parameters?

The parameters are

$\begin{gathered} \operatorname{mean}\text{ = }\mu=18.8 \\ \text{Standard Deviation = }\sigma=1.1 \end{gathered}$

We want to find

$p(\mu<17)$

Part B

Find the z score

The formula to use is given by

$z=\frac{\bar{X}-\mu}{\sigma}$$\begin{gathered} z=\frac{\bar{X}-\mu}{\sigma} \\ z=\frac{17-18.8}{1.1} \\ z=\frac{-1.8}{1.1} \\ z=-1.6363636363 \\ z=-1.64 \end{gathered}$

The construction of the standard normal curve is shown below

Part C

We use the standard normal table (from statistical table)

Thus, From statistical table

$p(z<-1.64)=0.05$