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?
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.
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