Question

For the questions 15-19, please use the following information.
The Arizona state lottery, Lotto, is played as follows: The player selects six numbers from the numbers 1-42 and buys a ticket for $1. There are six winning numbers, which are selected at random from the numbers 1-42. To win a prize, a Lotto ticket must contain three or more of the winning numbers. Following is a probability distribution for the number of winning numbers for a single ticket.

Number of winning numbers	0	1	2	3	4	5	6
Probability	0.3713060	0.4311941	0.1684352	0.0272219	0.0018014	0.0000412	0.0000002

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Question 151 pts

Determine the mean.

Group of answer choices

0.857143

3.000000

4.200000

0.336870

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Question 161 pts

Determine the standard deviation.

Group of answer choices

0.8032

0.6451

0.8571

0.43119

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Question 171 pts

If you buy one Lotto ticket, determine the probability that you win a price.

Group of answer choices

0.029

0.027

0.002

0.001

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Question 191 pts

If you have more than 1 winning numbers on a ticket, what is the probability you have 3 winning numbers on that ticket?

Group of answer choices

0.138

0.027

1.000

0.002

Answer 1

x	P(X=x)	xP(x)	x2P(x)
0	0.3713060	0.00000	0.00000
1	0.4311941	0.43119	0.43119
2	0.1684352	0.33687	0.67374
3	0.0272219	0.08167	0.24500
4	0.0018014	0.00721	0.02882
5	0.0000412	0.00021	0.00103
6	0.0000002	0.00000	0.00001
total		0.8571	1.3798
	E(x) =μ=	ΣxP(x) =	0.8571
	E(x2) =	Σx2P(x) =	1.3798
	Var(x)=σ2 =	E(x2)-(E(x))2=	0.645097
	std deviation=	σ= √σ2 =	0.80318

from above:

151) mean = 0.857143

161) standard deviation = 0.8032

171) probability that you win a price =0.029

181) probability you have 3 winning numbers on that ticket given more than 1 winning number

=0.0272219/0.1974999

=0.138