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Question

A certain tennis player makes a successful first serve $70\%$ of the time. Assume that each serve is independent of the others. She serves 80 times in a match. What 's the probability she makes at least 65 first serves?

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2Result exercise 29a:

$\mu=56$

$\sigma=4.0988$

The z-score is the value decreased by the mean, divided by the standard deviation:

$z=\dfrac{x-\mu}{\sigma}=\dfrac{65-56}{4.0988}\approx 2.20$

Determine the corresponding probability using table Z in appendix F:

$P(X\geq 65)=P(Z> 2.20)=1-P(Z<2.20)=1-0.9861=0.0139=1.39\%$

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