Question

1) A raffle offers one $1000.00 prize, one $500.00 prize, and five $200.00 prizes. There are 5000 tickets sold at $4 each. Find the expectation if a person buys one ticket.

2) The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first grade class is shown below.

Number of cartoons watched   X	0	1	2	3	4	5
Probability   P(X)	0.15	0.20	0.30	0.10	0.20	0.05

Give the standard deviation for the probability distribution.

Answer 1

1) ANSWER:

Expectation = 1000 * (1/5000) + 500 * (1/5000) + 200 * (4/5000) = 0.46 $

But price is 4 $

Hence expectation = 4 - 0.46 = 3.54 $

2) ANSWER:

σ² = E(x²) - (E(x))²

E(x) = Σx.p(x) = 0(0.15) + 1(0.2) + 2(0.3) + 3(0.1) + 4(0.2) + 5(0.05)

= 0.2 + 0.6 + 0.3 + 0.8 + 0.25 = 2.15

E(x²) = Σx².p(x) = 0(0.15) + 1(0.2) + 4(0.3) + 9(0.1) + 16(0.2) + 25(0.05)

= 6.75

--> σ² = 6.75 - 2.15² = 2.1275

--> σ = √2.1275 = 1.46

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