650 A standard chemistry examination administered nationally

6.50 A standard chemistry examination administered nationally by the American Chemical Society has a mean of Mu = 500 and a standard deviation of Sigma =90. What is the probability that the average score of a random sample of the examination scores of 25 students will be between 450 and 550?

Solution

The probability is

P(450<xbar<550) = P((450-500)/(90/sqrt(25)) <(xbar-mean)/(s/vn) <(550-500)/(90/sqrt(25)))

=P(-2.78<Z<2.78)

=0.9946 (from standard normal table)