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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's 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. The dotplot displays the number of second serves missed by the player out of the first 20 second serves in 100 simulated matches. ………………………… ******** ****** 3 4 5 6 1 2 Number of missed serves in simulated match Is there convincing evidence that the player misses more than 10% of her second serves? Why or why not? No, there is not convincing evidence that the player misses more than 10% of her second serves. Missing 5 out of 20 is better than expected. No, there is not convincing evidence that the player misses more than 10% of her second serves. Assuming the player makes 90% of her second serves, there is only a 7% chance that she would miss 5 or more of her first 20 second serves. No, the player could have just had a particularly unlucky streak. There is no way to determine the answer to this if we don't know how many times the player will serve overall during a tennis match. Yes, because 10% of 20 is 2 and most of the points on the dotplot fall at 2 or higher. This is evidence that the player misses more than 10% of her second serves.

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's 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. The dotplot displays the number of second serves missed by the player out of the first 20 second serves in 100 simulated matches. ………………………… ******** ****** 3 4 5 6 1 2 Number of missed serves in simulated match Is there convincing evidence that the player misses more than 10% of her second serves? Why or why not? No, there is not convincing evidence that the player misses more than 10% of her second serves. Missing 5 out of 20 is better than expected. No, there is not convincing evidence that the player misses more than 10% of her second serves. Assuming the player makes 90% of her second serves, there is only a 7% chance that she would miss 5 or more of her first 20 second serves. No, the player could have just had a particularly unlucky streak. There is no way to determine the answer to this if we don't know how many times the player will serve overall during a tennis match. Yes, because 10% of 20 is 2 and most of the points on the dotplot fall at 2 or higher. This is evidence that the player misses more than 10% of her second serves.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Simulation of Tennis Serve Accuracy** A professional tennis player claims to successfully deliver 90% of her second serves. Recently, she missed 5 out of her first 20 second serves in a match. To evaluate if this outcome is surprising given her claim, we can simulate the probability of missing 5 or more serves in her first 20 attempts assuming a 10% miss probability per serve. **Dotplot Analysis:** The dotplot illustrates the number of second serves missed out of the first 20 serves in 100 simulated matches. The x-axis represents the number of missed serves in the simulated match, ranging from 0 to 7. Each dot corresponds to the frequency of that number of missed serves occurring. **Interpretation of Results:** - The distribution is centered around 2 missed serves, indicating that missing around 2 serves is most common if the player’s claim is accurate. - A small number of simulations resulted in the player missing 5 or more of her first 20 serves. **Question for Analysis:** Is there sufficient evidence that the player misses more than 10% of her second serves? **Answer Options:** - No, missing 5 out of 20 is better than expected. - No, with only a 7% chance of missing 5 or more serves, there isn't convincing evidence against her claim. - No, it's possible the player had an unlucky streak. - Uncertain, without knowing the overall number of serves. - Yes, given 10% of 20 is 2, and many results show 2 or more missed serves, suggesting more than 10% misses. Engage with this activity by evaluating the dotplot and choosing the interpretation that aligns with your understanding of probability and statistical evidence.
Transcribed Image Text:**Simulation of Tennis Serve Accuracy** A professional tennis player claims to successfully deliver 90% of her second serves. Recently, she missed 5 out of her first 20 second serves in a match. To evaluate if this outcome is surprising given her claim, we can simulate the probability of missing 5 or more serves in her first 20 attempts assuming a 10% miss probability per serve. **Dotplot Analysis:** The dotplot illustrates the number of second serves missed out of the first 20 serves in 100 simulated matches. The x-axis represents the number of missed serves in the simulated match, ranging from 0 to 7. Each dot corresponds to the frequency of that number of missed serves occurring. **Interpretation of Results:** - The distribution is centered around 2 missed serves, indicating that missing around 2 serves is most common if the player’s claim is accurate. - A small number of simulations resulted in the player missing 5 or more of her first 20 serves. **Question for Analysis:** Is there sufficient evidence that the player misses more than 10% of her second serves? **Answer Options:** - No, missing 5 out of 20 is better than expected. - No, with only a 7% chance of missing 5 or more serves, there isn't convincing evidence against her claim. - No, it's possible the player had an unlucky streak. - Uncertain, without knowing the overall number of serves. - Yes, given 10% of 20 is 2, and many results show 2 or more missed serves, suggesting more than 10% misses. Engage with this activity by evaluating the dotplot and choosing the interpretation that aligns with your understanding of probability and statistical evidence.
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