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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.
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