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. What is the probability that in a one-game playoff, her score is more than 227?

Answer 1

Answer:

The probability that in a one-game playoff, her score is more than 227 is 0.4404.

Step-by-step explanation:

We are given that 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.

Let, X = scores over that period of time

X ~ N($\mu = 225, \sigma = 13^{2}$)

The z score probability distribution is given by;

          Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = average score

            $\sigma$ = standard deviation

So, probability that in a one-game playoff, her score is more than 227 is given by = P(X > 227)

    P(X > 227) = P( $\frac{X-\mu}{\sigma}$ < $\frac{227-225}{13}$ ) = P(Z > 0.15) = 1 - P(Z $\leq$ 0.15)

                                                      = 1 - 0.55962 = 0.4404

Therefore, probability that in a one-game playoff, her score is more than 227 is 0.4404.