Question

1.            Use the following table to calculate the expected value. The following table describes the possible outcomes and their associated probabilities.

x	P(x)
($20)	0.05
($5)	0.1
$0	0.15
$10	0.35
$15	0.2
$30	0.15

                The first 2 outcomes are losses (negative values).

                What is the expected value of this probability distribution?

                (1 point)

2.            In a certain school (enrollment in the school is well over 1000 students), 40% are male. If you randomly select 8 students:

                A.            What is the probability exactly 3 will be male?

                B.            What is the probability that at least 2 will be male?

                (1 point each = 2 points)

3.            In a certain hospital ER the average amount of patients that enter in a 15 minute interval is 3.6. If each 15 minute interval is independent of one another, and the amount of patients that show up in one 15 minute interval does not influence or change the number of patients that show up in any other 15 minute interval. Arrivals occur smoothly throughout each 15 minute interval. Answer the following questions:

A.            What is the probability that at most 2 patients will show up in a 15 minute interval?    

B.            What would be your new mean, if we were to use this information to figure out probabilities during a 5 minute interval?

C.            Using the new mean in part B, what is the probability that more than 1 patient will show up in a 5 minute interval?

Answer 1

1. $9.5 is the expected value of this probability distribution.

2. A. 0.2787 is the probability that exactly 3 will be male.

B. 0.8936 is the probability that at least 2 will be male.