Question

A company sells manure in 5 pound bags. However, customers usually buy it in bulk so the expected number of pounds that a person buys is 19.25 with a standard deviation of 5.76 . There is also a fixed tax cost for each bag. The profit for an order can be described as 75X-100, where X is the number of 5 pound bags a person buys. What is the standard deviation of this problem?

A. $332.00
B. $432.00
C $532.00
D. $1343.75
E $1400.00

Answer 1

The standard deviation of the problem is $332.00.

Step-by-step explanation:

To find the standard deviation of the problem, we need to calculate the standard deviation of the number of bags a person buys multiplied by the profit per bag. The standard deviation of the number of bags can be obtained by dividing the standard deviation of pounds bought by 5. The standard deviation of the profit can be calculated using the formula sd = sqrt((n * sd^2) + (mean^2 * sdp^2)), where sd is the standard deviation of the number of bags, n is the number of bags, sd^2 is the variance of the number of bags, mean is the mean of the number of bags, and sdp is the standard deviation of the profit per bag. Plugging in the values, we get sd = sqrt((19.25/5)^2 * 5.76^2 + (19.25)^2 * 0^2) = 332.00.