Finding the Mean, Variance, Standard Deviation of Sampling Distribution of the Sample Mean

Suppose that we will take a random sampleof size n from population having meanµ and standard deviationσ. For each of the following situations, find the mean, variance, and standard deviation of the samplingdistribution of the sample mean:

(a) µ = 12 , σ = 2.2 , n = 25 (Round your answers of “σ ” to 4 decimal places and “σ 2” to 3 decimal places.)
µ
σ 2
σ
——————————————————————————–

(b) µ = 510 , σ = .5 , n = 110 (Round your answers of “σ ” to 4 decimal places and “σ 2” to 3 decimal places.)
µ
σ 2
σ
——————————————————————————–

(c) µ = 5 , σ = .3 , n = 4
µ
σ 2
σ
——————————————————————————–

(d) µ = 110 , σ = 1.2 , n = 1,800 (Round your answers of “σ ” to 4 decimal places and “σ 2” to 3 decimal places.)
µ
σ 2
σ
——————————————————————————–

Answers

(a) µ = 12 , σ = 2.2 , n = 25 (Round your answers of “σ ” to 4 decimal places and “σ 2” to 3 decimal places.)

µ = 12
σ2 = (2.2)2/25 = 0.194
σ = √0.194 = 0.4405 …

The standard deviations of sampling distributions of the sample mean is examined.