One thousand raffle tickets are sold at $1 each. Three tickets will be drawn at random (without replacement), and each will pay $200 . Suppose you buy 5 tickets. (A) Create a payoff table for 0 , 1 , 2 , and 3 winning tickets among the 5 tickets you purchased. (If you do not have any winning tickets, you lose $5 ; if you have 1 winning ticket, you net $ 195 since your initial $5 will not be returned to you; and so on.) (B) What is the expected value of the raffle to you?
One thousand raffle tickets are sold at $1 each. Three tickets will be drawn at random (without replacement), and each will pay $200 . Suppose you buy 5 tickets. (A) Create a payoff table for 0 , 1 , 2 , and 3 winning tickets among the 5 tickets you purchased. (If you do not have any winning tickets, you lose $5 ; if you have 1 winning ticket, you net $ 195 since your initial $5 will not be returned to you; and so on.) (B) What is the expected value of the raffle to you?
Solution Summary: The author calculates the payoff table for 0,1,2, and 3 winning tickets among the 5 tickets bought from the one thousand raffle tickets sold at 1 each.
One thousand raffle tickets are sold at
$1
each. Three tickets will be drawn at random (without replacement), and each will pay
$200
. Suppose you buy
5
tickets.
(A) Create a payoff table for
0
,
1
,
2
,
and
3
winning tickets among the
5
tickets you purchased. (If you do not have any winning tickets, you lose
$5
; if you have 1 winning ticket, you net
$
195
since your initial
$5
will not be returned to you; and so on.)
(B) What is the expected value of the raffle to you?
Example 4 (Part 2) We can use Statkey to take 50 different random samples of size 20 each, find the mean of
each sample, and compute a confidence interval for each one. The graph of the sampling distribution of the means
is on the left below, and that of the 50 confidence intervals is on the right.
1. What does each dot on the left hand dotplot represent?
StatKey Sampling Distribution for a Mean
Percent with Internet Access (Countries) ▾
Show Data Table Edit Data
Choose samples of size n =
20
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Change Column(s)
Generate 1 Sample
Generate 10 Samples
Generate 100 Samples
Generate 1000 Samples
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Sampling Dotplot of Mean
Left Tail Two-Tail Right Tail
60
50
40
40
30
20
20
10
samples = 50
mean = 41.626
std. error = 5.089
:
.:
:
::
0
25
30
35
40
45
50
55
60
41.626
Data Plots
Confidence Intervals
95%->
Confidence Intervals
Coverage
48/50 = 96%
20
40
60
80
2. Circle the confidence intervals that failed to capture the true mean.
3. Circle the sample means that produced those…
Can you prove by induction on n for the following
Chapter 8 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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