The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of six per hour. (a) What is the probability that exactly two arrivals occur during a particular hour? (Round your answer to three decimal places.) (b) What is the probability that at least two people arrive during a particular hour? (Round your answer to three decimal places.) (c) How many people do you expect to arrive during a 45-min period? people

a) 0.045 = 4.5% probability that exactly two arrivals occur during a particular hour

b) 0.983 = 98.3% probability that at least two people arrive during a particular hour

c) 4.5 arrivals during a 45-min period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

Poisson process with a rate parameter of six per hour.

This means that . So

(a) What is the probability that exactly two arrivals occur during a particular hour?

This is P(X = 2).

0.045 = 4.5% probability that exactly two arrivals occur during a particular hour

(b) What is the probability that at least two people arrive during a particular hour?

Either less than two people arrive during a particular hour, or at least two do. The sum of the probabilities of these events is decimal 1. So

We want

In which

0.983 = 98.3% probability that at least two people arrive during a particular hour

(c) How many people do you expect to arrive during a 45-min period? people

An hour has 60 mins.

45/60 = 3/4.

So

4.5 arrivals during a 45-min period.

b or 2, just plug these equations into your graphing calculator then check the graph to see the image. if it matches up then that's your answer!