Chapter 11.5, Problem 25HP

To determine

To find: The set of real world data that appears to be normally distributed and then calculate the range of the values that is represent the middle 68%, the middle 95% and he middle 99.7% of the distribution.

Answer to Problem 25HP

The data is on scores per team in each game of first round of the NBA play-off. The value of 68% interval is $85.50<X<107.62$ , 95% interval is $74.44<X<118.68$ and 99.7% is $63.38<X<129.74$ .

Explanation of Solution

Consider that the data is on scores per team in each game of first round of the NBA play-off.

Consider the mean of the scores per team is 11.06. Then, according to the empirical normal distribution of the textbook the middle 68% of the distribution lie on the interval of,

  $\begin{array}{l}\left(96.56-11.06\right)<X<\left(96.56+11.06\right)\\ 85.50<X<107.62\end{array}$

Then, the middle 95% lie in the interval.

  $\begin{array}{l}\left(96.56-2\left(11.06\right)\right)<X<\left(96.56+2\left(11.06\right)\right)\\ 74.44<X<118.68\end{array}$

Then, the middle 99.7% lie in the interval.

  $\begin{array}{l}\left(96.56-3\left(11.06\right)\right)<X<\left(96.56+3\left(11.06\right)\right)\\ 63.38<X<129.74\end{array}$