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Double fault!A professional tennis player claims to get 90%of her second serves in. In a recent match, the player missed 5of her first 20second serves. Is this a surprising result if the player鈥檚 claim is true? Assume that the player has a 0.10probability of missing each second serve. We want to carry out a simulation to estimate the probability that she would miss 5or more of her first 20second 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 20second serves in simulated matches.

b. Explain what the dot at 6represents.

c. Use the results of the simulation to estimate the probability that the player would miss 5or more of her first 20second 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 0.10on each second serve, we expect about 1out of 10second serves to miss.

b. The number of serves missed in a simulated match of 20second serves among 100simulated 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" 6of the 100simulated matches result in 5or more second serve misses.

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

Step by step solution

01

Part (a) Step 1 : Given Information

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

02

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 20second works. This means that

0.10=110

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

03

Part (b) Step 1 : Given Information

We have to explain what the dot at 6represents.

04

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 20second serves among 100simulated matches is also shown. The dot at 6symbolises a trial in which the player failed to hit of the 20-second serves.
05

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 20second serves in a match.

06

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 20second serves among 100simulated matches is also provided. The dot plot then shows that there are six dots at 5and one dot at 6, indicating that 6of the 100simulated matches result in 55 or more second serve misses. Then,

6100=0.06

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

07

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.

08

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 20second serves among 100simulated matches. Thus, we have,

鈥冣赌10%of the 20second serve is 10%20=0.1020

=2

We then note that there are many dots in the dot plot at 2and to the left of 2which implies that is very common to have less than 2missed 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.

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