Question

Suppose the mean amount of cholesterol in eggs labeled “large” is 186 milligrams, with standard deviation 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

μ$\overline{X}$=μ=186

σ$\overline{X}$=σ/$\sqrt{n}$ =7/12=0.583

Z=(188−186)/0.583=3.43

P(184<$\overline{X}$<188)=P(-Z<x<Z)=P(-3.43<x<3.43)=0.9994