Question

1. Organizers of a concert are limiting ticket sales to a maximum of 4 tickets per customer. Past experience has shown that the probability distribution of the number of tickets purchased in these situations is:

Number of Tickets Purchased	Probability
1	0.1
2	0.3
3	0.2
4	0.4

What is the expected value of the number of tickets purchased? Include 1 decimal place in your answer.

2.

Kelsie works at a bicycle shop as a salesperson. The probability distribution of the number of bicycles Kelsie sells on a randomly selected day is shown below:

Number of Bicycles Sold	Probability
0	0.30
1	0.50
2	0.15
3	0.05

The mean for the number of bicycles sold is 0.95. What is the standard deviation? Round your answer to 2 decimal places.

Answer 1

1)

x	P(x)	x * P(x)
1	0.1	0.1
2	0.3	0.6
3	0.2	0.6
4	0.4	1.6
Sum	1	2.9

Mean = = X * P(X) = 2.9

the expected value of the number of tickets purchased = 2.9

2)

x	P(x)	x * P(x)	x2 * P(x)
0	0.3	0	0
1	0.5	0.5	0.5
2	0.15	0.3	0.6
3	0.05	0.15	0.45
Sum	1	0.95	1.55

Mean = = X * P(X) = 0.95

Standard deviation =

=X ² * P(X) - ²

=  1.55 - 0.95²

= 0.80