Question

9 a laboratory tested 72 chicken eggs and found that the mean amount of cholesterol was 240 milligrams with s=19.6 milligrams. construct a 95 percent confidence interval for the true mean cholesterol content, μ, of all such eggs.

Answer 1

Note that we're dealing with a sample here, specifically, 72 sample chicken eggs. Sample mean is 240 mg. Want 95% confidence interval.

Use the following formula for the 95% confidence interval of a sample:
sample std. dev.
sample mean plus or minus (1.602) ------------------------
sqrt(n)
19.6 mg
Here, this gives us 240 mg plus or minus (1.602) ---------------
sqrt(72)

which simplifies to 240 mg plus or minus (1.602) (2.310), or

240 mg plus or minus 3.7 mg

the 95th confidence interval for the true mean cholest. content is
(-236.3, 243.7).