A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is

Solution:

Given n(sample size) = 49

Population mean(μ) = 80

Standard Deviation(σ) = 7

Standard error of the mean = σx-bar = σ/√n = 7/√49 = 7/7 = 1

Standardizing the sample mean we have 

Z = (x-bar - μ)/σx-bar = (x-bar - μ)/σ/√n 

x-bar = 82

Z = (82 - 80)/1 = 2

Representing the above information as sampling distribution curve we have

If we refer to the z distribution table, the area represented by the shaded curve is given by the table

The shaded area shown above for z = 2 is equal to 0.4772

Hence the probability that the sample mean will be 82 is 0.4772 or 47.72%

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is

Summary:

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is 47.72% or 0.4772.