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

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