Question

In the past 30 days, Roger’s Rural Roundup has sold 8, 9, 10, or 11 lottery tickets. It never sold fewer than 8 or more than 11. The owner looked at the past 30 days to determine how many were sold each day. Eight lottery tickets were sold on 10 days, nine lottery tickets were sold on 12 days, 10 tickets sold on 6 days, and 11 tickets were sold on 2 days.

1) Develop a probability distribution table from the data (using a relative frequency approach… see powerpoint 2-27).

2) What is the expected value of the distribution? (powerpoint 2-30 and 2-31)

3) What is the variance of the distribution? (powerpoint 2-32 and 2-33)

PLEASE SHOW WORK! This is so I can learn how to do it please!

Answer 1

(1)

x	f	P(x) = Relative f	x * P(x)	x^2 * P(x)
8	10	0.3333	2.6667	21.33333
9	12	0.4000	3.6	32.4
10	6	0.2000	2	20
11	2	0.0667	0.7333	8.066667
Sum =	30	1	9	81.8

(2)

Expected value = ∑x * P(x) =  9

(3)

Variance = ∑x^2 * P(x) - (Expected value)^2 = 81.8 - 9^2 = 0.8