The mean weight of loads of coal placed in train cars by a l

The mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distributed, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight of those loads is more than 40.60 tons.

Solution

P(xbar>40.6) = P((xbar-mean)/(s/vn) >(40.6-43)/(8/sqrt(9)))

=P(Z>-0.9)

=0.8159 (from standard normal table)