A population has a standard deviation of 25 and a mean of 300. Given a random sample of size 100, how likely is it that the sample mean will be within +/- 5 of the population mean?
Answers
Given : A population has a standard deviation of 25 and a mean of 300. Given a random sample of size 100,
To Find : how likely is it that the sample mean will be within +/- 5 of the population mean?
Solution:
Mean = 300
Standard deviation of population = 25
Sample Size = 100
SE = Standard Error = Standard deviation of population / √Sample size
= 25/√100
= 2.5
SE = 2.5
sample mean will be within +/- 5
Hence between - 2SD and + 2SD
From Z score table :
0.0228 to 0.9772
Hence 0.9772 - 0.0228 = 0.9544
Hence 0.9544 or 95.44 % its likely to have sample mean will be within +/- 5 of the population mean
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