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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 5.1.20c
Chapter 5, Problem 5.1.20c

Using Probabilities for Significant Events


c. Which probability is relevant for determining whether 1 is a significantly low 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 1 is a significantly low number of matches. This involves comparing probabilities calculated in part (a) and part (b).
Step 2: Recall the concept of 'significantly low' events in probability. An event is considered significantly low if its probability is very small, typically less than or equal to a threshold such as 0.05 (5%).
Step 3: Review the probabilities calculated in part (a) and part (b). Part (a) likely involves calculating the probability of getting exactly 1 match, while part (b) might involve calculating the cumulative probability of getting 1 or fewer matches.
Step 4: Determine which probability is more relevant for assessing whether 1 match is significantly low. The cumulative probability from part (b) is typically used for this purpose, as it accounts for all outcomes up to and including the event in question.
Step 5: Conclude that the probability from part (b) is the relevant one for determining whether 1 match is significantly low, as it provides a broader context for evaluating the rarity of the event.

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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 1 match, is significantly low compared to expected outcomes.
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Calculating Probabilities in a Binomial Distribution

Significance Level

The significance level, often denoted as alpha (α), is a threshold used to determine whether a result is statistically significant. It represents the probability of rejecting the null hypothesis when it is true. Understanding this concept helps in assessing whether the observed number of matches is significantly low in the context of the probabilities calculated in parts (a) and (b).
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Step 4: State Conclusion Example 4

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions based on data analysis. It involves formulating a null hypothesis and an alternative hypothesis, then using sample data to determine which hypothesis is supported. This concept is crucial for evaluating whether the observed number of matches (1) is significantly low by comparing it against the expected outcomes derived from the previous parts.
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Step 1: Write Hypotheses
Related Practice
Textbook Question

Politics The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning the order in which candidates’ names appeared on voting ballots. Among 41 different ballots, Democrats were assigned the desirable first line 40 times. Assume that Democrats and Republicans are assigned the first line using a method of random selection so that they are equally likely to get that first line.


c. Find the probability of 40 or more first lines for Democrats.

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Textbook Question

In Exercises 9–16, use the Poisson distribution to find the indicated probabilities.


Births In a recent year (365 days), NYU-Langone Medical Center had 5942 births.


c. Find the probability that in a single day, there are no births. Would 0 births in a single day be a significantly low number of births?

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Textbook Question

One of Mendel’s famous experiments with peas resulted in 580 offspring, and 152 of them were yellow peas. Mendel claimed that under the same conditions, 25% of offspring peas would be yellow. Assume that Mendel’s claim of 25% is true, and assume that a sample consists of 580 offspring peas.


c. Find the probability of 152 or more yellow peas.


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Textbook Question

Expected Value for the Florida Pick 3 Lottery In the Florida Pick 3 lottery, you can bet \$1 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect \(500.


d. Find the expected value for a \)1 bet.

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Textbook Question

Expected Value in North Carolina’s Pick 4 Game In North Carolina’s Pick 4 lottery game, you can pay \(1 to select a four-digit number from 0000 through 9999. If you select the same sequence of four digits that are drawn, you win and collect \)5000.


d. Find the expected value.

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Textbook Question

Politics The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning the order in which candidates’ names appeared on voting ballots. Among 41 different ballots, Democrats were assigned the desirable first line 40 times. Assume that Democrats and Republicans are assigned the first line using a method of random selection so that they are equally likely to get that first line.

.

d. Which probability is relevant for determining whether 40 first lines for Democrats is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 40 first lines for Democrats significantly high?


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