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28 August, 17:21

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

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  1. 28 August, 20:41
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    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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