Question

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n equals = 62 ​, find the probability of a sample mean being less than 23.6 if mu μ equals = 24 and sigma σ equals = 1.21

Would the given sample mean be considered​ unusual?

Answer 1

Population mean μ = 24 and a standard deviation σ = 1.21

We want to find the probability of a sample mean being less than 23.6

P(xbar < 23.6) = P((xbar - µ)/ (σ/√n)) < (23.6 – 24)/ (1.21/sqrt(62))

             = P( Z < - 2.603)

               = 0.0047…….. (Using Statistical table)

The probability is 0.0047.

The given sample mean being less than 23.6 would be considered unusual because it has less than 5% probability.