Poisson: Deaths Currently, an average of 7 residents of the villa...

5. Binomial Distribution & Discrete Random Variables

Discrete Random Variables

Statistics

5. Binomial Distribution & Discrete Random Variables

Discrete Random Variables

1:17 minutes

Problem 5.R.10a

Textbook Question

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

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.

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.

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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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.