Question

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 overline x in attendance on those days in each sample. Calculate the mean and standard deviation of the sampling distribution of overline x You may round to one decimal place . mu overline x = Box students sigma overline x = Box students

Answer 1

Answer:

- Mean of sampling distribution = μₓ = 55.0 students.

- Standard Deviation of sampling distribution

= 1.8 students.

Explanation:

The Central limit theorem explains that for the sampling distribution obtained randomly from an independent population distribution, the mean is approximately equal to the population mean and the standard deviation of the sampling distribution is related to the population standard deviation through

σₓ = (σ/√n)

where σ = population standard deviation = 4

n = sample size = 5

Mean = population mean

μₓ = μ = 55 students.

Standard deviation

σₓ = (σ/√n) = (4/√5) = 1.789 students = 1.8 students to 1 d.p

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