Question

Shoppers at a mall have a mean weight of 70 kg with a standard deviation of 10 kg. An elevator at the mall holds a maximum of 6 people, and safety engineers are curious about the average weight of shoppers on a full elevator. Suppose that we take random samples of 6 shoppers and calculate the mean weight of the shoppers in each sample.

a. Calculate the mean and standard deviation of the sampling distribution of a You may round to one decimal place.

Answer 1

The average weight of shoppers on a full elevator is 70 kg, and the standard deviation is 4.08 kg.

The mean of the sampling distribution of the sample means will be equal to the mean of the population, which is 70 kg. This is because the sampling process does not change the mean of the population.

The standard deviation of the sampling distribution of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size, which is

10 kg /
`√((6))` = 4.08 kg.

Therefore, the mean of the sampling distribution is 70 kg and the standard deviation of the sampling distribution is 4.08 kg.