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Susan has been on a bowling team for 14 years. After examining all of her scores...

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, use an appropriate normal transformation to calculate the probability that her average score for the week is between 222 and 228.

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Answer #1

Solution :

Given that,

mean = \mu = 225

standard deviation = \sigma = 13

n = 16

\mu\bar x = \mu = 225

\sigma\bar x = \sigma / \sqrt n = 13 / \sqrt 16 = 3.25

P(222 < \bar x < 228)  

= P[(222 - 225) / 3.25 < (\bar x - \mu \bar x) / \sigma \bar x < (228 - 225) / 3.25)]

= P(-0.92 < Z < 0.92)

= P(Z < 0.92 ) - P(Z < -0.92)

Using z table,  

= 0.8212 - 0.1788

= 0.6424

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