Answer to Question #209375 in Statistics and Probability for mak

Question

The mean weight of loads of rock is 47.0 tons with a standard deviation of 6.0 tons. If 16 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 46.2 tons. Assume that the variable is normally distributed.

Answer 1

$\mu = 47.0 \\ \sigma=6.0 \\ n=16 \\ P(\bar{X}<46.2) = P(Z< \frac{46.2-47}{6.0/ \sqrt{16}} )\\ = P(Z< -0.533) \\ = 0.2970$