Answer to Question #349075 in Statistics and Probability for siobhan

Question

the average cholesterol of a certain canned goods is 180 milligrams, and the standard deviation is 12 milligrams. assume that the variable is normally distributed. if a sample of 16 canned goods is selected, what is the probability that the mean of the sample will be greater than 172 milligrams

Answer 1

$$P(X>172)=1-P(Z\le\dfrac{172-180}{12/\sqrt{16}})$$

$$=1-P(Z\le-2.6667)=0.99617$$