# Statistics

posted by
**Matt**
.

A specially equipped trauma emergency room at a hospital has been in operation for 40 weeks and has been used a total of 240 times. Assuming the weekly pattern of demand for this facility is Poission, compute the following:

1) The probability that the room is not used in a given week,

2) The probability that the room is used seven or more times in a week, and

3) The mean demand for a two week period.

Poisson distribution with a mean of m is this: P(x) = e^(-m) m^x / x!

For #1: 240/40 = 6 (average per week)

P(0) = e^(-6) 6^0 / 0! = 0.0025 (rounded value)

For #2: P(>=7) = 1 - P(<7) = 1 - [P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6)]

You might be able to use a table instead of computing these by hand.

For #3: The mean demand for a two week period = 12.