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?

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()

The z score probability distribution is given by;

          Z = ~ N(0,1)

where, = average score

             = 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( < ) = P(Z > 0.15) = 1 - P(Z 0.15)

                                                      = 1 - 0.55962 = 0.4404

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

b

step-by-step explanation:

b