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

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.

Accepted Answer

Welcome back, everyone. In a small city, an average of 15 cars are reported stolen each month. The probability distribution follows the Poisson model. What is the probability that on a given day no cars are reported stolen? A 0.6605. B 0.0665, C 0.7065, and D 0.6065. For this problem, we're going to use the poison probability distribution. It says that the probability of X being equals to lowercase x. is equal to lambda raises the power of X, multiplied by E raises the power of negative lambda divided by X factorial. Let's begin with Xs. Specifically, this is our random variable. It says that no cars are reported stolen, and this means that X is equal to 0. What is more important is that we're given the units of days, right? So, essentially our units would be cars per day. Meaning 0 cars are reported stolen or basically no cars are reported stolen in. One day or on a given day. And now let's identify lambda, which is the average number of cars stolen per day and we're given 15 cars per month. So we have to convert the units. We are going to take 15 cars and divide by 30 days in 1 month, assuming that one month has 30 days, right? So that would be 0.5 cars per day. Now that we have the same units, we can begin by writing the formula P X equals 0. Would be lambda, raise the power of X, so that's 0.5, raise to the power of 0, multiplied by E raise to the power of negative lambda or 0.5 divided by X factorial, which is 0 factorial. And this simplifies to E raises to the power of negative 0.5, which is 0.6065. Which corresponds to the answer choice. Thank you for watching.

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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).

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

Key Concepts

Poisson Distribution

Rate Parameter (λ)

Probability of No Events

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