Question

Andy Lee is the punter for the San Francisco 49ers. He had a stellar 2011 season with an average punt length of 50.9 yards with a standard deviation of 3.5. His punt distance follows a normal distribution. Andy Lee's first punt of the season was 66 yards. what is the z-score for this punt?A. -2.4B. 2.4C. 4.3D.5.5

Answer 1

The z-score of a normal distribution is defined by

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

where

`\begin{gathered} x\text{ is the score we want to find } \\ \mu\text{ is the mean value of the distribution} \\ \sigma\text{ is the standard deviation of the distribution} \end{gathered}`

Then, using the formula for the z-score in our problem we have

`Z=(66-50.9)/(3.5)=(15.1)/(3.5)=4.3`

Then the z score for that punt is 4.3.