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Directions: Please answer the following questions showing as much work as possible.More work means that I can see where you are going wrong and help you correct your mistakes.I can also award partial credit if I can see partially correct solutions.

The number of patients seen in the emergency room at a Lakeside Hospital in any given hour is a random variable represented by X.The probability distribution for this random variable is given in the table below.

X

10

11

12

13

14

P(X)

0.4

0.2

0.2

0.1

0.1

1.[5 points] Find the probability that in a given hour exactly 14 patients arrive.

2.[5 points] Find the probability that in a given hour more than 12 patients arrive.

3.[5 points] Find the mean of the probability distribution.

4.[5 points] Find the standard deviation of the probability distribution.

5.[10 points] When more than 12 patients arrive in a given hour, the ER finds itself short staffed.Define a new random variable Y = the number of hours in a day that the ER is short staffed.Describe the distribution of Y.(If you are at all unsure about the answer to this question, please contact me.You must have this correct before proceeding.)

6.[10 points] Find the probability that in a given day the ER is short staffed exactly 4 hours.

7.[10 points] What is the expected number of hours that the ER will be short staffed in a given day?

8.[10 points] What is the standard deviation for the number of hours the ER will be short staffed in a given day?

9.[10 points] Find the probability that in a given day, the ER is short staffed for no more than 4 hours.

10.[10 points] Define a new random variable W = the number of hours in a 240 hour block of time that the ER is short staffed.Describe the distribution of W.

11.[20 points] Using a normal approximation, find the probability that in a given 240 hour period, the ER is short staffed for no more than 40 hours.