Plastic bags used for packaging produce are manufactured so

Plastic bags used for packaging produce are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 2 pounds per square inch. What is the probability that a sample of 16 such bags will have an average breaking strength less than 6 pounds per square inch? (Choose the closest answer. Answers are rounded to the fourth decimal place).

Solution

the probability that a sample of 9 such bags will have an average breaking strength less than 6 pounds per square inch is

P(xbar<6) = P((xbar-mean)/(s/vn) <(6-5)/(1/sqrt(9)))

=P(Z<3) = 0.9987 (from standard normal table)