Question

Suppose that the middle 95% of average scores in the NBA per player per game fall between 8.18 and 31.34. Give an approximate estimate of the standard deviation of the number of the points scored. Assume the points scored has a normal distribution.

Answer 1

An approximate estimate of the standard deviation of the number of the points scored per game is of 5.79.

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Suppose that the middle 95% of average scores in the NBA per player per game fall between 8.18 and 31.34.

This means that there is 4 standard deviations within this interval. So

`4s = 31.34 - 8.18`

`4s = 23.16`

`s = (23.16)/(4)`

`s = 5.79`

An approximate estimate of the standard deviation of the number of the points scored per game is of 5.79.