Which of the following is the correct formula to find the variance of any Poisson random variable "x"?

There is an average (mean) of 3 road construction projects that take place at any one time in a city. Find the probability that exactly 5 road construction projects are currently taking place. [Assume road construction projects take place randomly.]

Given that on average (mean) 10 people are killed by sharks worldwide each year, find the probability that 1 or 2 people will be killed by sharks next year.

[Assume shark attacks occur randomly.]

A mean number of 0.6 major hurricanes strike the U.S. mainland each year. Find the probability that more than one major hurricane will strike the U.S. mainland in a given year, assuming that hurricane landfalls occur randomly.

A rental car service center company has 5 cars available for rental each day. Assume that each car is rented out for the whole day and that the number of cars rented out each day is randomly distributed with a mean of 2. Find the probability that the company cannot meet the demand for cars on any one day.

Can this situation be modeled with a Poisson random variable?

A mall kiosk sees an average (mean) of 8 customers per hour. Customers are most likely to arrive during the evening hours. Let "x" = the number of customers that arrive next hour.

Can this situation be modeled with a Poisson random variable?

A mall kiosk sees an average (mean) of 8 customers per hour. Customers are equally likely to arrive at any time. Let "x" = the number of customers that arrive next hour.

A tropical island near a fault line has experienced 12 major earthquakes in the last 200 years.

Assuming that earthquakes occur randomly, find the probability that this island will experience at least one major earthquake in the next decade (10 years.)

A tropical island near a fault line has experienced 12 major earthquakes in the last 200 years.

Let "x" = the number of earthquakes this island experiences next year. Assuming that earthquakes here occur randomly, find the standard deviation of "x."

A busy McDonald's restaurant serves an average (mean) of 33 customers per hour during peak hours.

Assuming that customers arrive randomly and that each employee can serve one customer every two minutes, how many employees must this restaurant have on staff during peak hours in order to ensure that its capacity exceeds demand at least 99% of the time?

A tropical island near a fault line has experienced 12 major earthquakes in the last 200 years.

Assuming that earthquakes occur randomly, find the probability that this island will not have any major earthquakes in the next 40 years.

Which of the following conditions must be met in order for a random variable "x" to be considered Poisson? Check all that apply.

Poisson distributions are... (check all that apply)

A veteran truck driver has been driving for 30 years. During that time, he has been in 18 accidents. Find the probability that next year he will be in multiple accidents. Assume that accidents occur randomly to this driver.

A residential street sees a mean 18 cars per hour pass by a certain location during rush hour.

Which of the following Events is most likely to occur during the next rush hour?

A residential street sees a mean 18 cars per hour pass by a certain location during rush hour.

Which of the following Events is least likely to occur during the next rush hour?

Review: What is an outcome?

Review: The letters that form the word MATHEMATICS are placed in a bowl.

If these letters are drawn from the bowl one by one at random, and then placed in the order in which they were drawn, what is the probability that they actually spell this word?

Review: The set of all possible outcomes of a trial is known as the ________________ of that trial.

Review: You roll two fair dice. What is the probability that one of the dice comes up 4, and the other comes up with a number (strictly) less than 3?

[Hint: Draw a diagram or try to list all of the outcomes in the Event.]

Review: You flip a nickel three times.

Find the probability that all flips will land on tails.

Review: You can only use the Power Rule for Events in Sequence if they all have the same probability and are all ______________________ in relation to each other.

Review: Three students are chosen at random from a college class that has 27 male and 30 female students. What is the probability of choosing one male and two females? Round to the nearest percent.

Review: In the data set

{33, 25, 42, 25, 31, 37, 46, 29, 38} ,

What is the third quartile of the data?

A jewelry store averages 2.9 sales per hour. Assuming that sales occur randomly, if this store is open eight hours tomorrow, what is the probability it will have between 20 and 25 sales (inclusive)?

Integration: A shop has a mean of 3.2 sales per hour. What is the probability that, tomorrow, this shop will make its first sale in the third hour that it is open?