Q. 10 Double fault!聽A professional te... [FREE SOLUTION]

魅影直播

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 魅影直播 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 5: Q. 10 (page 310)

Double fault!A professional tennis player claims to get $90 %$ of her second serves in. In a recent match, the player missed $5$ of her first $20$ second serves. Is this a surprising result if the player鈥檚 claim is true? Assume that the player has a $0.10$ probability of missing each second serve. We want to carry out a simulation to estimate the probability that she would miss $5$ or more of her first $20$ second serves.
a. Describe how to use a random number generator to perform one trial of the simulation. The dot plot displays the number of second serves missed by the player out of the first $20$ second serves in simulated matches.
b. Explain what the dot at $6$ represents.
c. Use the results of the simulation to estimate the probability that the player would miss $5$ or more of her first $20$ second serves in a match.
d. Is there convincing evidence that the player misses more than $10 %$ of her second serves? Explain your answer.

Short Answer

Expert verified

a. The probability of missing the second serve is $0.10$ on each second serve, we expect about $1$ out of $10$ second serves to miss.

b. The number of serves missed in a simulated match of $20$ second serves among $100$ simulated matches is shown in a dot plot.

c. In the dot plot, there are six dots at $5$ and one dot at $6$ , indicating that data-custom-editor="chemistry" $6$ of the $100$ simulated matches result in $5$ or more second serve misses.

d. The fact that there are many dots in the dot plot at $2$ and to the left of $2$ indicates that it is highly typical to have fewer than $2$ failed serves in a simulated match, implying that the player misses at most $10 %$ of her second serves.

Step by step solution

Part (a) Step 1 : Given Information

We have to describe how to use a random generator to perform one trial of the simulation.

Part (a) Step 2 : Simplification

It is unsurprising that a professional tennis player claims to hit $90 %$ of her second serves. The chance of missing a second serve is now $0.10$ . As a result, we'll run a simulation to see how $20$ second works. This means that

$0.10 = \frac{1}{10}$

Because the chance of missing the second serve is $0.10$ , we should expect around $1$ out of every $10$ second serves to be missed. Let's utilise a random generator to generate $20$ digits at random, ranging from $0$ to $90$ to $9$ , with zero being a miss and the other digits representing no miss.

Part (b) Step 1 : Given Information

We have to explain what the dot at $6$ represents.

Part (b) Step 2 : Simplification

It is unsurprising that a professional tennis player claims to hit

90 %

of her second serves. A dot plot of the number of serves missed in a simulated match of

20

second serves among

100

simulated matches is also shown. The dot at

6

symbolises a trial in which the player failed to hit of the

20

-second serves.

Part (c) Step 1 : Given Information

We have to use the result of the simulation to estimate the probability that the player would miss five or more of her first $20$ second serves in a match.

Part (c) Step 2 : Simplification

A professional tennis player claims to be able to get one of her second serves in. A dot plot of the number of serves missed in a simulated match of $20$ second serves among $100$ simulated matches is also provided. The dot plot then shows that there are six dots at $5$ and one dot at $6$ , indicating that $6$ of the $100$ simulated matches result in 55 or more second serve misses. Then,

$\frac{6}{100} = 0.06$

We conclude that missing $5$ or more of the first $20$ second serves in a match has a chance of $0.06$ .

Part (d) Step 1 : Given Information

We have to explain is there a convincing evidence that the player misses more than $10 %$ of her second serves.

Part (d) Step 2 : Simplification

It is given that a professional tennis player claims to get $90 %$ of her second serves in. And the dot plot is given which shows the number of serves missed in a simulated match of $20$ second serves among $100$ simulated matches. Thus, we have,

鈥冣赌� $10 %$ of the $20$ second serve is $10 % 脳 20 = 0.10 脳 20$

$= 2$

We then note that there are many dots in the dot plot at $2$ and to the left of $2$ which implies that is very common to have less than $2$ missed serves in a simulated match and thus it is very likely that the player misses at most $10 %$ of her second serves. Thus there is not convincing evidence that the player misses more than $10 %$ of her second serves.