Question

Use the 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval that is expected to contain about 95% of the data values.

1. A bell-shaped distribution with mean 250 and standard deviation 27 .
The interval is _____________ to ____________.

Answer 1

The interval is 196 to 304.

Explanation:

According to the 95% rule, in a symmetric bell-shaped distribution, 95% of the data is comprised within two standard deviations above or below the mean value of the data set.

For a distribution with a mean of 250 and standard deviation of 27, the lower and upper boundaries of the 95% interval are:

`L=250 -(2*27) =196\\U=250 +(2*27) =304`

The interval is 196 to 304.