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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.R.10a
Chapter 5, Problem 5.R.10a

Poisson: Deaths Currently, an average of 7 residents of the village of Westport (population 760) die each year (based on data from the U.S. National Center for Health Statistics).
a. Find the mean number of deaths per day.

Verified step by step guidance
1
Step 1: Understand the problem. The problem involves a Poisson distribution, which is used to model the number of events (in this case, deaths) occurring in a fixed interval of time. The given average number of deaths per year is 7.
Step 2: Recall the formula for converting the mean (λ) from one time unit to another. To find the mean number of deaths per day, divide the annual mean by the number of days in a year. Assume a year has 365 days unless otherwise specified.
Step 3: Write the formula for the mean number of deaths per day: λ_daily = λ_annual / 365.
Step 4: Substitute the given value of λ_annual (7 deaths per year) into the formula: λ_daily = 7 / 365.
Step 5: Simplify the expression to find the mean number of deaths per day. This will give you the average daily death rate for the village.

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Key Concepts

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

Poisson Distribution

The Poisson distribution is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, given a known average rate of occurrence. It is particularly useful for modeling rare events, such as deaths in a population, where the events occur independently of each other.
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Intro to Frequency Distributions

Mean

The mean, often referred to as the average, is a measure of central tendency that is calculated by summing all values in a dataset and dividing by the number of values. In the context of the question, the mean number of deaths per year can be converted to a daily mean by dividing the annual average by the number of days in a year.
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Calculating the Mean

Rate Conversion

Rate conversion involves adjusting a rate from one time frame to another, such as converting annual rates to daily rates. This is done by dividing the annual figure by the number of time units in a year, typically 365 days, to find the average occurrence per day, which is essential for understanding daily trends in data.
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Calculating the Mean Example 1
Related Practice
Textbook Question

In Exercises 1–5, assume that 4.2% of workers test positive when tested for illegal drugs (based on data from Quest Diagnostics). Assume that a group of ten workers is randomly selected.


Workplace Drug Testing Find the mean and standard deviation for the numbers of workers in groups of ten who test positive for illegal drugs.

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Textbook Question

In Exercises 1–5, assume that 4.2% of workers test positive when tested for illegal drugs (based on data from Quest Diagnostics). Assume that a group of ten workers is randomly selected.


Workplace Drug Testing If none of the ten workers tests positive for illegal drugs, is that a significantly low result?

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Textbook Question

In Exercises 1–5, assume that 4.2% of workers test positive when tested for illegal drugs (based on data from Quest Diagnostics). Assume that a group of ten workers is randomly selected.


Workplace Drug Testing Find the probability that at least one of the ten workers tests positive for illegal drugs.

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Textbook Question

In Exercises 1–5, assume that 4.2% of workers test positive when tested for illegal drugs (based on data from Quest Diagnostics). Assume that a group of ten workers is randomly selected.


Workplace Drug Testing Find the probability that exactly two of the ten workers test positive for illegal drugs.

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Textbook Question

Is the mean found in the preceding exercise a statistic or a parameter?

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Textbook Question

In Exercises 6–10, refer to the accompanying table, which describes the numbers of adults in groups of five who reported sleepwalking (based on data from “Prevalence and Comorbidity of Nocturnal Wandering In the U.S. Adult General Population,” by Ohayon et al., Neurology, Vol. 78, No. 20).

Significant Events Is 4 a significantly high number of sleepwalkers in a group of 5 adults? Explain.

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