Question

Assume the cost of an extended? 100,000 mile warranty for a particular SUV follows the normal distribution with a mean of ?$1,320

and a standard deviation of ?$105

Complete parts ?(a) through ?(d) below.

?a) Determine the interval of warranty costs from various companies that are one standard deviation around the mean.

The interval of warranty costs that are one standard deviation around the mean ranges from $ ___ to ___

?b) Determine the interval of warranty costs from various companies that are two standard deviations around the mean. The interval of warranty costs that are two standard deviations around the mean ranges from $___ to ___

?(Type integers or decimals. Use ascending? order.)

?c) Determine the interval of warranty costs from various companies that are three standard deviations around the mean.

The interval of warranty costs that are three standard deviations around the mean ranges from$___ to ___

?(Type integers or decimals. Use ascending? order.)

?d) An extended? 100,000 mile warranty for this type of vehicle is advertised at ?$1,740.

Based on the previous? results, what conclusions can you? make?

A. The $1,740 cost of this warranty is slightly higher than average due to the fact that it is more than three standard deviations above the mean.

B. This warranty is better quality than warranties offered by competing companies due to the fact that it is more than three standard deviations above the mean.

C. The ?$1,740 cost of this warranty is much higher than average due to the fact that it is more than three standard deviations above the mean.

D.The ?$1,740 cost of this warranty must be an error in the advertisement because a data value cannot be more than three standard deviations from the mean.

Answer 1

a)as one std deviation values from mean =1320 -/+ 105 =1215 to 1425

The interval of warranty costs that are one standard deviation around the mean ranges from 1215 to 1425

b)

The interval of warranty costs that are two standard deviations around the mean ranges from 1110 to 1530

c)

The interval of warranty costs that are three standard deviations around the mean ranges from 1005 to 1635

d)

C. The ?$1,740 cost of this warranty is much higher than average due to the fact that it is more than three standard deviations above the mean