A small school with 60 total students records how many of their students attend school on each of the 180 days in a school year. The mean number of students in attendance daily is 55 students and the standard
deviation is 4 students. Suppose that we take random samples of 5 school days and calculate the mean
number of students ĉ in attendance on those days in each sample.
Calculate the mean and standard deviation of the sampling distribution of

The answer is below

Explanation:

Given that the mean of the attendance of the population (μ) = 55 students, and the standard deviation (σ) = 55 students

If repeated random samples of a given size n are taken from a population with a population mean of μ and the population standard deviation of σ,  then the mean of the sample distribution () is population mean μ, while the standard deviation of the sample distribution () is the population standard deviation divided by the square root of the sample size.

Given a random sample (n) of 5 days, hence:

mean of sampling distribution () = μ = 55 students

standard deviation of the sampling distribution = =