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Ch. 5 - Discrete Probability Distributions
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 5 - Discrete Probability DistributionsProblem 5.1.19c
Chapter 5, Problem 5.1.19c

Using Probabilities for Significant Events


c. Which probability is relevant for determining whether 3 is a significantly high number of matches: the result from part (a) or part (b)?

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Step 1: Understand the context of the problem. The question is asking which probability is relevant for determining whether 3 is a significantly high number of matches. This involves comparing probabilities calculated in parts (a) and (b).
Step 2: Recall the concept of 'significantly high' events in probability. A significantly high number of matches typically refers to a situation where the probability of observing that number or more is very small, often less than a threshold such as 0.05.
Step 3: Review the probabilities calculated in parts (a) and (b). Part (a) likely involves the probability of observing exactly 3 matches, while part (b) might involve the cumulative probability of observing 3 or more matches.
Step 4: Determine which probability is relevant. To assess whether 3 is significantly high, the cumulative probability from part (b) (P(X ≥ 3)) is typically used, as it considers the likelihood of observing 3 or more matches.
Step 5: Conclude that the probability from part (b) is relevant for determining whether 3 is a significantly high number of matches, as it aligns with the definition of 'significantly high' events in probability.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability Distribution

A probability distribution describes how the probabilities are distributed over the values of a random variable. It provides a framework for understanding the likelihood of different outcomes, which is essential for determining whether a specific result, like 3 matches, is significant in the context of the overall data.
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Significance Level

The significance level, often denoted as alpha (α), is a threshold used in hypothesis testing to determine whether to reject the null hypothesis. It represents the probability of making a Type I error, which occurs when a true null hypothesis is incorrectly rejected. Understanding this concept helps in assessing whether the observed number of matches is statistically significant.
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Step 4: State Conclusion Example 4

Comparative Analysis

Comparative analysis involves evaluating different sets of data or results to draw conclusions about their significance. In this context, it requires comparing the probability results from parts (a) and (b) to determine which provides a more relevant basis for assessing whether 3 matches is significantly high.
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Related Practice
Textbook Question

In Exercises 29 and 30, assume that different groups of couples use the XSORT method of gender selection and each couple gives birth to one baby. The XSORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.


Gender Selection Assume that the groups consist of 36 couples.


c. Is the result of 26 girls a result that is significantly high? What does it suggest about the effectiveness of the XSORT method?

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Textbook Question

Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula.


Guessing Answers Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT), typically use multiple choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions.


c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made?

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Textbook Question

Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).


Using Probabilities for Significant Events


b. Find the probability of getting 2 or more matches.


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Textbook Question

Salary Negotiations In a Jobvite survey, 2287 adult workers were randomly selected and asked about salary negotiations.


b. Among those who negotiated salary, 84% received higher pay. How many received higher pay?


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Textbook Question

In Exercises 25–28, find the probabilities and answer the questions.


Internet Voting Based on a Consumer Reports survey, 39% of likely voters would be willing to vote by Internet instead of the in-person traditional method of voting. For each of the following, assume that 15 likely voters are randomly selected.


c. Find the probability that at least one of the selected likely voters would do Internet voting.

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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



e. Find the standard deviation.

f. Find the variance.


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