Question

Suppose the mean amount of cholesterol in eggs labeled “large” is 186 milligrams, with a standard deviation of 7 milligrams. Find the probability that the mean amount of cholesterol in a sample of 144 eggs will be within 2 milligrams of the population mean.

Answer 1

$$P(184\le X\le 188)=P(Z\le\dfrac{188-186}{7/\sqrt{144}})$$ $$-P(Z<\dfrac{184-186}{7/\sqrt{144}})$$ $$=P(Z\le 3.42857)-P(Z<-3.42857)$$

$$=0.99970-0.00030=0.9994$$