Question

Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation of 0.2 feet. A sample of 37 men’s step lengths is taken.Step 2 of 2 : Find the probability that the mean of the sample taken is less than 2.3 feet. Round your answer to 4 decimal places, if necessary.

Answer 1

Given:

`\begin{gathered} mean(\mu)=2.5 \\ standard-deviation(\sigma)=0.2 \\ n=37 \end{gathered}`

To Determine: The probability that the mean of the sample taken is less than 2.3 feet.

Solution

`\begin{gathered} P(x<2.3) \\ z=(x-\mu)/(\sigma) \end{gathered}`
`\begin{gathered} z=(2.3-2.5)/(0.2) \\ z=-(0.2)/(0.2) \\ z=-1 \end{gathered}`

The probability would be

`\begin{gathered} P(x<-1)=0.15866 \\ P(x<-1)\approx0.1587 \end{gathered}`

Hence, the probability that the mean f the sample taken is less than 2.3 feet is approximately 0.1587