Answer to Question #336396 in Statistics and Probability for Katherine

Question

Suppose the amount of a popular sport drink in bottles leaving the filling machine has a normal distribution with mean 101.5 milliliters (mL) and standard deviation 1.6. If 36 bottles are randomly selected, find the probability that the mean content is less than 102.1 mL 

Answer 1

$$P(X<102.1)=P(Z<\dfrac{102.1-101.5}{1.6/\sqrt{36}})$$

$$=P(Z<2.25)\approx0.9878$$