Ch. 5 - Normal Probability Distributions

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 5 - Normal Probability Distributions

Problem 5.C.4a

Chapter 5, Problem 5.C.4a

Use the probability distribution in Exercise 3 to find the probability of randomly selecting a game in which DeMar DeRozan had (a) fewer than four personal fouls,

Verified step by step guidance

Identify the probability distribution provided in Exercise 3. This could be a discrete probability distribution, such as a probability mass function (PMF), or a table listing the probabilities for each possible number of personal fouls.

Determine the range of values that correspond to 'fewer than four personal fouls.' This means you are interested in the probabilities for 0, 1, 2, and 3 personal fouls.

Sum the probabilities for the values identified in the previous step. Mathematically, this can be expressed as: P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).

If the probabilities are given in a table, locate the corresponding values for P(X = 0), P(X = 1), P(X = 2), and P(X = 3) and add them together.

Verify that the total probability for all possible outcomes in the distribution equals 1. This ensures the distribution is valid and that your calculations are based on accurate data.

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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 of a random variable are distributed across its possible values. It provides a mathematical function that gives the likelihood of each outcome, allowing us to understand the behavior of the variable. In this context, it helps in determining the probability of DeMar DeRozan having fewer than four personal fouls based on the distribution of his fouls in previous games.

Random Variable

A random variable is a numerical outcome of a random phenomenon, which can take on different values based on chance. In this case, the random variable is the number of personal fouls committed by DeMar DeRozan in a game. Understanding random variables is crucial for calculating probabilities and making inferences about the data.

Cumulative Probability

Cumulative probability refers to the probability that a random variable takes on a value less than or equal to a specific value. It is essential for answering the question about the likelihood of DeRozan having fewer than four personal fouls, as it involves summing the probabilities of all outcomes that meet this criterion. This concept allows us to assess the overall likelihood of a range of outcomes.

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Related Practice

Textbook Question

Finding a z-Score Given an Area In Exercises 23–30, find the indicated z-score.

Find the positive z-score for which 12% of the distribution’s area lies between and z.

Textbook Question

Describe the inflection points on the graph of a normal distribution. At what x-values are the inflection points located?

Textbook Question

In Exercises 1–4, a population has a mean mu and a standard deviation sigma. Find the mean and standard deviation of the sampling distribution of sample means with sample size n.

Mu = 790, sigma =48, n = 250

Textbook Question

A survey of adults in the United States found that 61% ate at a restaurant at least once in the past week. You randomly select 30 adults and ask them whether they ate at a restaurant at least once in the past week. (Source: Gallup)

c. Is it unusual for exactly 14 out of 30 adults to have eaten in a restaurant at least once in the past week? Explain your reasoning.

Textbook Question

Forty-nine percent of U.S. adults think that human activity such as burning fossil fuels contributes a great deal to climate change. You randomly select 25 U.S. adults. Find the probability that the number who think that human activity contributes a great deal to climate change is (a) exactly 12,

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Textbook Question

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