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 were 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.

2. What is the expected value of the distribution?

3. What is the variance of the distribution?

Answer 1

Solution:-

1.)

Probability distribution:-

x(No. of Tickets)	Frequency	P(x) = Relative Frequency
8	10	0.3333
9	12	0.4
10	6	0.2
11	2	0.0667
Total	30	1

2.)

x(No. of Tickets)	Frequency	P(x) = Relative Frequency	x * P(x)	x2* P(x)
8	10	0.3333	2.6667	21.3312
9	12	0.4	3.6	32.4
10	6	0.2	2	20
11	2	0.0667	0.7337	8.0707
Total	30	1	9	81.80

Expected value = ∑x * P(x)

=  9 ...ans

3.)

Variance = ∑x²* P(x) - (Expected value)²

= 81.8 0- 9²

  = 0.80 ...ans