Question

1. One thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and cash prizes are to be awarded as follows: 1 prize of $100, 3 prizes of $50, and 5 prizes of $20. What is the expected value of this raffle if you buy 1 ticket?

2. Suppose 10% of the high school students are late for school.What is the probability that exactly 1 out of 5 students will be late for school? If we randomly select 50 students, what is the expected number of students who will be late for school? What is the standard deviation?

Answer 1

(1) probability distribution table

x(net prize)	P(X)
100-1 = 99	1/1000
50-1 = 49	3/1000
20-1 = 19	5/1000
-1	1-9/1000 = 991/1000

Expected value =

= $99*(1/1000) + $49*(3/1000) + 19*(5/1000) - $1*(991/1000)

= $0.099 + $0.147 + $0.095 - $0.991

= - $0.65 (expected value for one ticket)

(2) sample size n = 5

probability p = 0.10

To find P(X=1)

using binomial formula

Expected value = N*p, where N = 50 and p = 0.10

E[x] - 50*0.10 = 5

and

standard deviation =