/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 10 Double fault!聽A professional te... [FREE SOLUTION] | 91影视

91影视

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Scrabble In the game of Scrabble, each player begins by randomly selecting 7tiles from a bag containing 100tiles. There are 42vowels, 56consonants, and 2blank tiles in the bag. Cait chooses her 7tiles and is surprised to discover that all of them are vowels. We want to perform a simulation to determine the probability that a player will randomly select 7vowels.

a. Describe how you would use a table of random digits to carry out this simulation.

b. Perform one trial of the simulation using the random digits given. Copy the digits onto your paper and mark directly on or above them so that someone can follow what you did.

c. In 2of the 1000trials of the simulation, all 7tiles were vowels. Does this result give convincing evidence that the bag of tiles was not well mixed?

The security system in a house has two units that set off an alarm when motion is

detected. Neither one is entirely reliable, but one or both always go off when there is

motion anywhere in the house. Suppose that for motion in a certain location, the

probability that detector A goes off and detector B does not go off is 0.25, and the

probability that detector A does not go off is 0.35. What is the probability that detector

B goes off?

a.0.1b.0.35c.0.4d.0.65e.0.75

Teachers and college degrees Select an adult at random. Define events D: person has earned a college degree, and T: person鈥檚 career is teaching. Rank the following probabilities from smallest to largest. Justify your answer.

P(D)P(T)P(DT)P(TD)

Due to a hit A very good professional baseball player gets a hit about 35% of the time

over an entire season. After the player failed to hit safely in six straight at-bats, a TV

As one commentator said, 鈥淗e is due for a hit.鈥 Explain why the commentator is wrong.

Treating low bone density Fractures of the spine are common and serious

among women with advanced osteoporosis (low mineral density in the bones). Can taking

strontium ranelate help? A large medical trial was conducted to investigate this question.

Researchers recruited 1649women with osteoporosis who had previously had at least one

fracture for an experiment. The women were assigned to take either strontium ranelate or a

placebo each day. All the women were taking calcium supplements and receiving standard

medical care. One response variable was the number of new fractures over 3years.

a. Describe a completely randomized design for this experiment.

b. Explain why it is important to keep the calcium supplements and medical care the same

for all the women in the experiment.

c. The women who took strontium ranelate had statistically significantly fewer new

fractures, on average, than the women who took a placebo over a 3year period. Explain

what this means to someone who knows little statistics.

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.