A tennis player usually makes a successful first serve 69% of the time.She buys a new racket hoping that it will improve her success rate.When she first tests her new racket she makes 4 first serves in a row.Is this evidence that with the new racket her success rate has improved? In other words,is a streak like this unusual for her? Explain.
A)Yes; if her success rate were still 69%,she would have only a 0.92% chance of making 4 shots in a row.That's an unusual result.
B)No; if her success rate were still 69%,she would have a 22.7% chance of making 4 shots in a row.That's not an unusual result.
C)Yes; if her success rate were still 69%,she would have only a 2.8% chance of making 4 shots in a row.That's an unusual result.
D)No; if her success rate were still 69%,she would have a 27.6% chance of making 4 shots in a row.That's not an unusual result.
E)Yes; if her success rate were still 69%,she would have only a 22.7% chance of making 4 shots in a row.That's an unusual result.

Question

Quizplus · Accepted Answer

If her success rate were still 69%, the probability of making 4 successful serves in a row is 0.69^4 = 0.227, or 22.7%. This is not an unusual result, so it does not provide strong evidence that her success rate has improved.

A Tennis Player Usually Makes a Successful First Serve 69