The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. if you select a random sample of 9 tennis balls, what is the probability that the sample mean is between 2.62 and 2.64 inches

For us to calculate for the probability of picking 2.62 and 2.64 in 9 balls we proceed as follows;

The z score is given by:

z = (x-mean) / s. d

z score of 2.62 will be:

z = (2.62-2.63) / 0.03

=-0.3333

the probability associated with the above z-score is:

P (2.62) = 0.3707

The z-score of 2.64 will be:

z = (2.64-2.63) / 0.03

z=0.3333

The probability associated with this z-score will be:

P (0.3333) = 0.6293

therefore the probability of obtaining a sample mean between 2.62 and 2.64 will be:

0.6293-0.3333

=0.296

thus the answer is 0.296