Question

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.

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