Question

Assume the cost of an extended​ 100,000 mile warranty for a particular SUV follows the normal distribution with a mean of ​$1,330 and a standard deviation of ​$75. Complete parts ​(a) through ​(d) below.

Question content area bottom Part 1 ​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 ​$enter your response here to ​$enter your response here. ​(Type integers or decimals. Use ascending​ order.)

Part 2 ​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 ​$enter your response here to ​$enter your response here. ​(Type integers or decimals. Use ascending​ order.)

Part 3 ​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 ​$enter your response here to ​$enter your response here. ​(Type integers or decimals. Use ascending​ order.)

Part 4 ​d) An extended​ 100,000 mile warranty for this type of vehicle is advertised at ​$1,630. Based on the previous​ results, what conclusions can you​ make?

A. 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.

B. The ​$1,630 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.

C. The ​$1,630 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 ​$1,630 cost of this warranty is slightly higher than average due to the fact that it is more than three standard deviations above the mean.

Answer 1

The interval of warranty costs that are one, two, and three standard deviations around the mean can be calculated using the formula (mean +/- (standard deviation * number of standard deviations)). The cost of the warranty ($1,630) is much higher than average because it is more than three standard deviations above the mean.

Step-by-step explanation:

Part 1: To determine the interval of warranty costs that are one standard deviation around the mean, we need to calculate the values that are one standard deviation above and below the mean.

The mean cost is $1,330 and the standard deviation is $75. One standard deviation above the mean is $1,330 + $75 = $1405, and one standard deviation below the mean is $1,330 - $75 = $1,255.

Therefore, the interval of warranty costs that are one standard deviation around the mean ranges from $1,255 to $1,405.

Part 2: To determine the interval of warranty costs that are two standard deviations around the mean, we multiply the standard deviation by 2.

Two standard deviations above the mean: $1,330 + (2 * $75) = $1,480

Two standard deviations below the mean: $1,330 - (2 * $75) = $1,180

The interval of warranty costs that are two standard deviations around the mean ranges from $1,180 to $1,480.

Part 3: To determine the interval of warranty costs that are three standard deviations around the mean, we multiply the standard deviation by 3.

Three standard deviations above the mean: $1,330 + (3 * $75) = $1,555

Three standard deviations below the mean: $1,330 - (3 * $75) = $1,105

The interval of warranty costs that are three standard deviations around the mean ranges from $1,105 to $1,555.

Part 4: Based on the previous results, we can conclude that option C is the most accurate. The cost of the warranty ($1,630) is much higher than average because it is more than three standard deviations above the mean.