Download X -1 3 5 P(X) 0.3 0.2 0.5 X 2 3 4 5 P(X) 0.1 0.3 0.5 0.1 X 0 1 2 3 4 5 P

Practice Problems: Sec 8-5, 9-1, 9-2
1. Find the expected value of the random variable.
X
P(X)
-1
0.3
3
0.2
5
0.5
2. Find the expected value of the random variable.
X
P(X)
2
0.1
3
0.3
4
0.5
5
0.1
3. A business bureau gets complaints as shown in the following table.
Find the expected number of complaints per day.
X
0
P(X) 0.04
1
0.11
2
0.21
3
0.33
4
0.19
5
0.12
4. Find the expected
value for the
random variable X
having this
probability function:
5. Find the expected value for the random variable X having this PDF:
6. A contractor is considering a sale that promises a profit of $23,000
with a probability of 0.7 or a loss (due to bad weather, strikes, etc.)
of $13,000 with a probability of 0.3. What is the expected profit?
7. John buys one $5 raffle ticket (out of a total of 500 sold in all). If a single
randomly selected winner gets a $100 prize, what are John’s expected
winnings?
8. Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the
prize for the winning ticket is to be $500.
What are your expected winnings?
9. A raffle offers a first prize of $1000, 2 second prizes of $300 and 20 third
prizes of $10 each. If 1000 tickets are sold at 50 cents each, find the
expected winnings for a person buying 1 ticket.
10. Two cards are drawn with replacement from a deck of cards and the
number of black cards is noted. If X is the random variable representing
the number of black cards drawn, construct the PDF.
11. Find the expected payback for a game in which you bet $6 on any
number from 0 to 399 and if your number comes up, you get $1000.
12. One option in a roulette game is to bet $2 on red. (There are 18 red
compartments, 18 black compartments and two compartments that are
neither black nor red.) If the ball lands on red, you get to keep the $2
you paid to play the game and you are awarded $2. If the ball lands
elsewhere, you are awarded nothing and the $2 bet is collected. Find
the expected payback for this game if you bet $2 on red.
13. Find the mean for the following numbers:
10.2, 7.1, 7.3, 8.4, 8.6.
14. Find the median for the following numbers: 10.2, 7.1, 7.3, 8.4, 8.6.
15. Find the standard deviation for the following numbers:
10.2, 7.1, 7.3, 8.4, 8.6.
16. Find the range for the following numbers: 10.2, 7.1, 7.3, 8.4, 8.6.
17. Find the median for the following numbers: 42, 18, 12, 33, 75, 22, 18, 35
18. Find the mode for the following numbers: 42, 18, 12, 33, 75, 22, 18, 35
19. Use the table below to find the
(a) mean, (b) median, (c) mode, and (d) standard deviation.
VALUE
16
17
23
28
36
FREQUENCY
2
3
4
5
1
20. Using the employment information in the table,
find the mean years of service for the grouped data.
Years of Service
1–5
6 – 10
11 – 15
16 – 20
21 – 25
26 - 30
Frequency
5
20
25
10
5
3
21. Find the standard deviation for the grouped data. (Round to nearest tenth.)
COLLEGE UNITS
FREQUENCY
0–4
4
5–9
3
10 - 14
6
15 - 19
3
20 - 24
5
22. A medical lab tested 8 samples of human blood for acidity on the pH
scale with the results below. What percentage of the data is within the
given standard deviations of the mean? (Round to the nearest whole
percentage.) 7.5 7.1 7.4 7.3 7.2 7.5 7.4 7.2
(a) ___% of the data is within 1 standard deviation of the mean.
(b) ___% of the data is within 2 standard deviations of the mean.
23. Chebyshev's Theorem states that for any set of numbers, the
fraction that will lie within k standard deviations of the mean is
at least
.
(a) Using this result, find the fraction of all the numbers of a data set that
must lie within 3 standard deviations of the mean.
(b) Find the fraction of all the numbers of a data set with a mean of 60
and standard deviation 4 that must lie between 52 and 68.