Question

A donut shop that specializes in unique donuts made from potatoes wants to learn more about their business costs. Past data reveals that the cost for fifty pounds of potatoes has a mean of $75 with standard deviation $13. The normal distribution for the population is shown by the dotted black line.

The donut shop plans to take a random sample of 31 such fifty pound bags of potatoes and will calculate the mean cost of the sample to compare to the known cost. Compute the mean and standard deviation of the sampling distribution of sample means for a sample of size 31. Round your answers to the nearest tenth.

Answer 1

The mean of the sampling distribution of sample means for a sample of size 31 is the same as the population mean, which is $75.

The standard deviation of the sampling distribution of sample means can be calculated using the formula:

standard deviation = population standard deviation / square root of sample size

Plugging in the given values, we get:

standard deviation = 13 / sqrt(31) = 2.3 (rounded to the nearest tenth)

Therefore, the mean of the sampling distribution of sample means is $75 and the standard deviation is $2.3.