Question

Refer to the variable on the number of miles driven. the mean is 830.11 and the standard deviation is 42.19 miles. estimate the number of buses traveling more than 900 miles. compare that number with the actual value.

Answer 1

The proportion of buses traveling more than 900 miles would be 0.0485; multiply this by the total number of buses and you will have your answer.

We find the z-score associated with 900 miles:

z = (X - μ)/σ = (900-830.11)/42.19 = 1.66

Using a z-table (http://www.z-table.com) we see that the area under the curve to the left of this, less than this, is 0.9515.  This means that the area under the curve to the right of this, greater than this, would be 1-0.9515 = 0.0485.