Textbook Question
Significant For 100 births, P(exactly 56 girls) and P(56 or more girls) Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question?
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Ch. 5 - Discrete Probability Distributions
Triola14th EditionElementary StatisticsISBN: 9780137366446
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Table of contents
- Ch. 1 - Introduction to Statistics88
- Ch. 2 - Exploring Data with Tables and Graphs70
- Ch. 3 - Describing, Exploring, and Comparing Data66
- Ch. 4 - Probability112
- Ch. 5 - Discrete Probability Distributions109
- Ch. 6 - Normal Probability Distributions122
- Ch. 7 - Estimating Parameters and Determining Sample Sizes107
- Ch. 8 - Hypothesis Testing75
- Ch. 9 - Inferences from Two Samples94
- Ch. 10 - Correlation and Regression80
- Ch. 11 - Goodness-of-Fit and Contingency Tables29
- Ch. 12 - Analysis of Variance42
Chapter 5, Problem 5.CRE.3a
Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.
a. If 1 of the 945 challenges is randomly selected, what is the probability that it resulted in an overturned call?
Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the probability that a randomly selected challenge resulted in an overturned call. This is a probability problem where we use the formula for probability: P(Event) = (Number of favorable outcomes) / (Total number of outcomes).
Step 2: Identify the favorable outcomes. From the table, the number of challenges that resulted in an overturned call is the sum of 'Challenge Upheld with Overturned Call' for both men and women. Add 160 (men) and 95 (women) to get the total number of overturned calls.
Step 3: Identify the total number of outcomes. The total number of challenges made is given as 945 in the problem statement.
Step 4: Write the probability formula. Substitute the values into the formula: P(Overturned Call) = (Total number of overturned calls) / (Total number of challenges).
Step 5: Simplify the fraction to express the probability. Divide the total number of overturned calls by the total number of challenges to get the probability. Leave the result in fraction or decimal form as required.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability
Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it is used to determine the chance that a randomly selected challenge from the total number of challenges resulted in an overturned call. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.
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Introduction to Probability
Favorable Outcomes
Favorable outcomes refer to the specific results that align with the event of interest in a probability scenario. In this case, the favorable outcomes are the challenges that resulted in overturned calls, which total 255. Understanding how to identify and count these outcomes is crucial for calculating the probability accurately.
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Guided course
06:00The Binomial Experiment
Total Outcomes
Total outcomes represent the complete set of possible results in a probability experiment. For this question, the total number of challenges made is 945. Knowing the total outcomes is essential for determining the probability, as it serves as the denominator in the probability formula, allowing for a comparison between favorable and total outcomes.
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04:04Fundamental Counting Principle
Related Practice
Textbook Question
Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.
0 0 1 2 17 28 21 8
c. Find the mode.
d. Find the range.
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Textbook Question
Identifying Probability Distributions. In Exercises 7–14, determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Fear of Heights The table lists results from a survey of 285 subjects who were asked, “Are you afraid of heights in tall buildings?” The results are from USA Today.
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Textbook Question
Kentucky Pick 4 In the Kentucky Pick 4 lottery game, you can pay \$1 for a “straight” bet in which you select four digits with repetition allowed. If you buy only one ticket and win, your prize is \$2500.
b. If you play this game once every day, find the mean number of wins in years with exactly 365 days.
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Textbook Question
Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.
0 0 1 2 17 28 21 8
i. What is the level of measurement of the data: nominal, ordinal, interval, or ratio?
j. Are the data discrete or continuous?
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Textbook Question
Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.
0 0 1 2 17 28 21 8
a. Find the mean.
b. Find the median.
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