Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

5. Binomial Distribution & Discrete Random Variables

Discrete Random Variables

Statistics

5. Binomial Distribution & Discrete Random Variables

Discrete Random Variables

Previous problemNext problem

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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

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.

Watch next

Master Intro to Random Variables & Probability Distributions with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 5.5 per year, as in Example 1; and proceed to find the indicated probability.

a. Find the probability that in a year, there will be 10 hurricanes.

Textbook Question

b. In a 118-year period, how many years are expected to have 10 hurricanes?

Textbook Question

Find the mean of the random variable x described in the preceding exercise.

Textbook Question

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

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).

b. Find the probability that on a given day, there are no deaths.

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).

c. Find the probability that on a given day, there is more than one death.

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.

a. Find the mean number of births per day.

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.

b. Find the probability that in a single day, there are 16 births.

Show more practices

Download the Mobile app

Privacy

Do not sell my personal information

Accessibility

Patent notice

Sitemap

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.

Key Concepts

Poisson Distribution

Mean

Rate Conversion

Watch next

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.