Question

A cost to ship a package is $8.50 plus $.16 per ounce. That is if C = cost of shipping a package, then C = 8.50 + .16U where U is the number of ounces. If the average number of ounces is 21 and the standard deviation is 5.5, what is the mean and standard deviation of the cost?

Answer 1

Given the equation:

`C=8.50+0.16U`

Where:

C is the cost of shipping a package

U is the number of ounces.

Given:

Average number of ounces = 21

Standard deviation = 5.5

Let's find the mean and standard deviation of the cost.

To find the mean of the cost, substitute the mean of the ounces for U and evaluate.

Substitute 21 for U:

`\begin{gathered} C=8.50+0.16(21) \\ \\ C=8.50+3.36 \\ \\ C=11.86 \end{gathered}`

Therefore, the mean of the cost is $11.86

To find the standard deviation of the cost, substitute the standard deviation of the ounces for U and evaluate.

Substitute 5.5 for U:

`\begin{gathered} C=8.50+0.16(5.5) \\ \\ C=8.50+0.88 \\ \\ C=9.38 \end{gathered}`

The standard deviation of the cost is $9.38.

ANSWER:

• Mean of the cost = 11.86

,

• Standard deviation of the cost = 9.38