Question

(Explained in steps please)
A vending machine operator has determined that the number of candy
bars sold per week by a certain machine is a random varlable with mean
125 and standard deviation 7. His profit on each bar sold is $0.25, and it
costs him $5.00 per week to maintain the machine and rent the space
for it. Which of the following gives the correct mean and standard deviation for Y = the profit he earns from this machine in a randomly
selected week?

Answer 1

Using multiplication of variable by a constant, it is found that the correct mean and standard deviation for Y are given by:

• D. Mean = $26.25, Standard deviation = $1.75.

Multiplication:

• When a variable is multiplied by a constant, both the mean and the standard deviation are multiplied by this constant.

In this problem:

• The variable is the number of candies sold, which has mean 125 and standard deviation 7.

• The constant is the profit, which is of $0.25.

Hence:

$M_Y = 125(0.25) = 31.25$

$S_Y = 7(0.25) = 1.75$

Also, from the mean, we have to subtract the cost per week, hence:

$M_Y = 31.25 - 5 = 26.25$

Hence, the correct option is:

• D. Mean = $26.25, Standard deviation = $1.75.

To learn more about multiplication of variable by a constant, you can take a look at https://brainly.com/question/25639778