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).