Question

Butterworth, Missouri, is trying to increase its tourism, a great source of revenue. Among other things, Butterworth prides itself on its temperate climate. The tourism department would like to include in its glossy new brochure the middle range of temperatures that occur on 90% of the days there. A check with the National Weather Service finds that the average temperature in Butterworth is 76 degrees with a standard deviation of 5.7 (the temperatures were normally distributed). Help the tourism department by finding the two temperatures that cut off the middle 90% of temperatures in Butterworth.

Answer 1

Is expected that 90% of the time the temperature in Butterworth will be between 66.6 deg F and 85.37 deg F.

Explanation:

The middle range of temperatures that occur on 90% of the days (upper limit and lower limit) can be calculated as:

`UL=\mu+z*\sigma\\\\LL=\mu-z*\sigma`

For a 90% interval, z is equal to 1.6449,

`UL=\mu+z*\sigma=76+1.6449*5.7=76+9.376=85.376\\\\LL=\mu-z*\sigma=76-1.6449*5.7=76-9.376=66.624`

Is expected that 90% of the time the temperature in Butterworth will be between 66.6 deg F and 85.37 deg F.