Download Page 1 1. (12 points) The weight of bags of peanuts

Math 166, MWF Fall 2012-copyright Joe Kahlig
Page 1
1. (12 points) The weight of bags of peanuts were normally distributed, with a mean of 45 oz and a
standard deviation of 4.5 oz.
(a) If 320 bags of peanuts are selected, approximately how many bags will weigh at least 47 oz?
Compute out a numerical answer.
(b) What is the probability that a randomly selected bag will weigh 44.5 oz? Compute out a
numerical answer.
(c) What is the probability that a randomly selected bag will weigh between 40 oz and 46 oz?
Compute out a numerical answer.
2. (6 points) The Athletic Department has an id code for its members. The code consists of the letter
combinations FBA (football), BAS (baseball), BSK ( basketball), SCR (soccer), or TRK ( track)
followed by 4 digits with the first digit being odd. How many codes are possible?
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Page 2
Math 166, MWF Fall 2012-copyright Joe Kahlig
3. (6 points) Your Mom has decided to display your high school trophies, listed
to the right. Assume that all of the trophies are distinct. How many ways
can these trophies be placed in a row if a soccer trophy is at both ends of
the shelf and the other trophies are grouped together by their sport?
trophies
2 soccer
2 basketball
5 track
6 tennis
4. (7 points) 50 people are applying for 10 jobs as lifeguards at a local beach. A group of seven friends
are among those that applying. What is the probability that exactly 3 of the friends will be hired as
lifeguards?
5. (12 points) A box contains some balls(listed below). A sample of 7 balls is to be picked from the box.
Box
10 red
4 yellow
6 green
(a) In how many ways can a sample be selected so that at least 5 of the balls will be green?
(b) In how many ways can you get exactly 4 red or exactly 3 yellow?
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Math 166, MWF Fall 2012-copyright Joe Kahlig
6. (12 points) Use the histogram for the random variable X to compute the following.
probability
0.35
(a) E(X) =
0.3
0.25
(b) median =
0.2
(c) population standard deviation =
0.15
0.1
0.05
(d) variance =
1
2
3
4
5
6
7
8
9
X
7. (3 points) Find the mode for the random variable X.
X
frequency
3
4
4
4
6
12
7
3
8
12
10
3
8. (4 points) X is a continuous random variable with a mean of 50 and a standard deviation 3. What
values of X are within 4 standard deviations of the mean?
9. (8 points) A box contains a collection of marbles(colors and types listed below). Let the random
variable X be the number of marbles drawn from the box until a yellow marble is drawn. Marbles are
drawn without replacement.
box
5 red
10 green
15 yellow
(a) What are the valid values of X?
(b) Compute P (X = 2).
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Math 166, MWF Fall 2012-copyright Joe Kahlig
Page 4
10. (4 points) How many different ways can 3 A’s, 5 B’s and 2 a’s be placed in a row?
11. (5 points) The random variable X has a mean of 20 and a standard deviation of 3. Use Chebychev’s
inequality to estimate P (14.6 ≤ X ≤ 25.4)
12. (10 points) A binomial experiment is repeated 50 times and p = 0.4.
(a) What is the probability of getting exactly 30 failures?
(b) What is the probability of getting at least 18 and fewer than 26 successes?
Compute out a numerical answer.
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Math 166, MWF Fall 2012-copyright Joe Kahlig
Page 5
13. (4 points) The scores of an exam are normally distributed with an average of 68 with a standard
deviation of 21. Find the lowest grade that a student could get on the exam that would count as a B.
The top 12% will get an A and the next 21% will get a B. Compute out a numerical answer.
14. (7 points) A game cost $3 to play. To play the game you toss an unfair coin, P (H) = 0.6. If you get
a tails then you lose the game. For a heads you draw one bill from a box that has one $5 dollar bill
and two $10 dollar bills. Let X be the net winnings of a player.
(a) Find the probability distribution of X.
(b) Compute the expected value of the game.
(c) Explain what the expected values means in context of the game.
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