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Ch. 4 - Discrete Probability Distributions
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 4 - Discrete Probability DistributionsProblema 4.Q.2a
Capitolo 4, Problema 4.Q.2a

The table lists the number of wireless devices per household in a small town in the United States.
Table showing the number of wireless devices per household and corresponding household counts in a small town.
a. Construct a probability distribution.

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Step 1: Calculate the total number of households by summing all the values in the 'Number of households' row. This will be the denominator for calculating probabilities.
Step 2: For each number of wireless devices (0, 1, 2, 3, 4, 5), divide the corresponding number of households by the total number of households to calculate the probability for each outcome. Use the formula: \( P(X = x) = \frac{\text{Number of households for } x}{\text{Total number of households}} \).
Step 3: Construct the probability distribution table. The table should have two columns: one for the number of wireless devices (0, 1, 2, 3, 4, 5) and another for the corresponding probabilities calculated in Step 2.
Step 4: Verify that the sum of all probabilities equals 1. This is a key property of a probability distribution and ensures correctness.
Step 5: Interpret the probability distribution. For example, identify which number of wireless devices is most likely (highest probability) and which is least likely (lowest probability).

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Probability Distribution

A probability distribution describes how the probabilities are distributed over the values of a random variable. In this context, it represents the likelihood of each household having a specific number of wireless devices. The probabilities are calculated by dividing the number of households for each category by the total number of households.
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Calculating Probabilities in a Binomial Distribution

Relative Frequency

Relative frequency is the ratio of the number of times an event occurs to the total number of trials or observations. In constructing a probability distribution from the table, relative frequency is used to determine the probability of each number of wireless devices by taking the count of households for each device number and dividing it by the total number of households.
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Intro to Frequency Distributions

Cumulative Frequency

Cumulative frequency is the sum of the frequencies for all categories up to a certain point. While not directly required for constructing a basic probability distribution, understanding cumulative frequency can help in analyzing the data further, such as determining the proportion of households with a certain number of devices or fewer.
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Creating Frequency Polygons
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Domanda del libro di testo

In Exercises 21–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities

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The five-year survival rate of people who undergo a liver transplant is 75%. The surgery is performed on six patients. (Source: Mayo Clinic)

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The table lists the number of wireless devices per household in a small town in the United States.

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