A laboratory tested 86 chicken eggs and found that the mean amount of cholesterol wasx= 228 mg. Assume that the population standard deviation is known to be 21 mg.

(a) Why are we allowed to assume that thesampling distributionin this problem is approximately normal?

The population is normally distributed.

The population standard deviation is known.

The sample size is large enough.

The margin of error is unknown.

(b) Construct a 95% confidence interval for the true mean cholesterol content,, of all such eggs.Round your answers to two decimal places.

lower limit

upper limit

margin of error

(c) Interpret your results in the context of this problem.

(1) We can be 95% certain that the true mean cholesterol for the population is inside the interval

found in part (b).

(2) can be 95% certain that the true mean cholesterol for the sample is outside the interval found in part (b).

We can be 95% certain that the true mean cholesterol for the population is outside the interval found in part (b).

(3) can be 95% certain that the true mean cholesterol for the sample is inside the interval found in part (b).

(d) Find the sample size necessary for an 95% confidence level with a maximal margin of errorE= 3.5for the mean cholesterol content.