Chapter 5.1, Problem 10E

(a)

To determine

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

Explanation of Solution

It is given that a professional tennis player claims to get $90\%$ of her second serves in. Now, the probability of missing a second serve is $0.10$ . So, we will carry out a simulation that $20$ second serves. This implies,

  $0.10=\frac{1}{10}$

Since the probability of missing the second serve is $0.10$ on each second serve, we expect about $\text{1 out of 10}$ second serves to miss. Let us now use a random generator to randomly generate $20$ digits from $\text{0 to 9}$ , where zero represents a miss and the other digits represents no miss.

(b)

To determine

To explain what the dot at $6$ represents.

Answer to Problem 10E

One trial in the simulation where the player missed $\text{6 of the 20}$ second serves.

Explanation of Solution

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 $\text{20}$ second serves among $\text{100}$ simulated matches. The dot at $6$ represents one trial in the simulation where the player missed $\text{6 of the 20}$ second serves.

(c)

To determine

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.

Answer to Problem 10E

  $0.06$ .

Explanation of Solution

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 $\text{20}$ second serves among $\text{100}$ simulated matches. We then note that there are six dots at $\text{5}$ and one dot at $\text{6}$ in the dot plot which implies that $\text{6 of the 100}$ simulated matches results in $\text{5}$ or more misses of the second serves. Then,

  $\begin{array}{l}\frac{6}{100}\\ =0.06\end{array}$

We then implies that the probability of missing $\text{5}$ or more of the first $20$ second serves in a match is $0.06$ .

(d)

To determine

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

Answer to Problem 10E

No, there is no convincing evidence.

Explanation of Solution

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 $\text{20}$ second serves among $\text{100}$ simulated matches. Thus, we have,

  $\begin{array}{l}\text{10\% of the 20 second serve is}\\ 10\%\times 20\\ =0.10\times 20\\ =2\end{array}$

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.