Question

Suppose that X is the number of cars per minute that passed through a certain intersection and that X has a poisson distribution if the mean of X is equal to 9 cars. What is the standard deviation of x?

Answer 1

The standard deviation of X is 3 cars.

Step-by-step explanation:

The Poisson distribution is a discrete probability distribution that is used to estimate the probability of a given number of events occurring in a fixed time period. The mean of X, which is 9 cars, is equal to the variance of X, and so the standard deviation of X is equal to the square root of 9, or 3 cars. This is because the standard deviation of a Poisson distribution is equal to the square root of the mean.

The Poisson distribution is commonly used in the field of statistics to model the number of events occurring in a given period of time. It has been used to model the number of cars passing through an intersection, the number of phone calls received by a business, and the number of people attending an event. In each case, the Poisson distribution can be used to estimate the probability of a certain number of events occurring in a given period of time.

The Poisson distribution is also commonly used in the field of mathematics to model the number of events occurring in a given period of time. In this case, the mean of X, which is 9 cars, is equal to the variance of X, and so the standard deviation of X is equal to the square root of 9, or 3 cars. This is because the standard deviation of a Poisson distribution is equal to the square root of the mean.

In conclusion, the standard deviation of X is 3 cars. This is because the mean of X is equal to the variance of X, and the standard deviation of a Poisson distribution is equal to the square root of the mean.