Answer to Question #316400 in Statistics and Probability for sach

Question

The average cholesterol content of a 100-gram bar of a certain brand of butter is 215 mg with a standard deviation of 15 mg. If a sample of twenty-five 100-gram bars of butter is selected, find the probability that the sample mean is less than 220 mg. Assume that the variable is normally distributed.

Answer 1

$P(\bar X<220)=P(<\frac{220-215}{\frac{15}{\sqrt{25}}})=P(Z<1.67)=0.9525.$