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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.
<em>Let, X = scores over that period of time</em>
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.