Question

The Orange County Fair offers raffle tickets to its guests. Four guests will win $500 prizes, six guests will win $50 prizes, and thirteen guests will win $13 prizes. There were 90 tickets sold for $7 each.

a) Construct a probability distribution for the data. Select an answer (No commas and from least to greatest) $ $ $ $ Select an answer (No commas) $ $ $ $ Select an answer (Write as a decimal rounded to two decimal places)

b) Calculate E ( X ) (same as μ ), σ 2 , and σ .

Population Mean: Select an answer = Population Variance: Select an answer = (round to two decimal places) Population Standard Deviation: Select an answer = (round to two decimal places)

Answer 1

a) Using the given frequency for each winning amount and the total frequency of 90, the probability distribution of profits is computed here as:

P(X = -7 + 500 = 493) = 4/90 = 2/45
P(X = -7 + 50 = 43) = 6/90 = 1/15
P(X = -7 + 13 = 6) = 13/90
P(X = -7) = (90 - 4 - 6 - 13) / 90 = 67/90

This is the required PDF for X here.

b) The computations are made using the following table here:

X	P(x)	xP(x)	x^2P(x)
493.0	0.0	21.9	10802.2
43.0	0.1	2.9	123.3
6.0	0.1	0.9	5.2
-7.0	0.7	-5.2	36.5
	1.0	20.4	10967.1

The expected value, variance and standard deviation here are computed as:

These are the required values here.