Question

A water treatment plant needs to maintain the pH of the water in the reservoir at a certain level. To monitor this, they take 2 oz. of water at 37 locations every hour, measure the pH at each of those locations, and find their average. If the pH level of the reservoir is ok, the results at each location will have varying results, with an average pH of 8.5 and a standard deviation of 0.22. If the pH level of the reservoir is ok, what is the probability that the sample average is LESS than 8.47?

Answer 1

here std error of mean =std deviation/sqrt(n)=0.22/sqrt(37)=0.036

from nomal distribution z score =(X-mean)/std error

hence  probability that the sample average is LESS than 8.47=P(Xbar<8.47)=P(Z<(8.47-8.5)/0.036)

=P(Z<-0.83)=0.2033