Question

Suppose the monthly charges for cell phone plans are normally distributed with mean mu equals $ 70 and standard deviation sigmaequals​$16. ​(a) Draw a normal curve with the parameters labeled. ​(b) Shade the region that represents the proportion of plans that charge less than ​$54. ​(c) Suppose the area under the normal curve to the left of Xequals​$54 is 0.1587. Provide an interpretation of this result.

Answer 1

a) The picture with the normal distribution is attached.

b) The picture with the normal distribution with the region X<54 shaded is attached.

c) The area under the normal curve to the left of X=$54 is 0.1587.

This means that there is a probability P=0.1587 that a randomly picked monthly charge for a cell phone plan is under $54.

It can also be interpreted that approximately 15.87% of the cell phone plans have a monthly charge that is less than $54.

Explanation: