Unformatted text preview: Math 111, Section0102 Exam 3 C. Hauck Name______________________________ Summer, 2003
Directions: Answer the following questions. In order to receive full credit, you must show your work. Your
answers must be legible and your explanation should include complete sentences. N 0 books or notes are allowed but
you may use a calculator. You have 80 minutes to take the exam. When you are ﬁnished, please make sure that
you rewrite by hand and sign the honor pledge on the front of your exam booklet. 1. (16 points) Suppose that you are given a standard six—sided die that is loaded. Let the random variable X be
the number rolled with the following probabilities: 1
Probability P(Xt=w) 0.2 0.3 . (a) Find the mean and standard deviation of X. (b) Draw a histogram of P (X = :16) vs. 01:. Include labels for the axes and tick marks. (c) Suppose you pay three dollars to play a game with the same loaded die. You roll the die once and receive
a payment in dollars equal to what you IlOll. For example, if you roll a two, then you get back two dollars.
Let Z be the random variable that describes your winnings. Find E (Z) . Is this a game you would like
to play? Explain. 2. (14 points) Suppose that you are given the same die as in Problem #1 and that you roll it ﬁve times. (a) Find the probability that you get an even number three of the five times. Find the odds.
(b) Find the probability that you get a multiple of three at most twice. Find the odds. 3. (15 points) At a children’s party, kids “bob for apples”. There are 30 apples total, ten of which are marked.
Ten children each take a turn and remove one; apple (which they keep) from the tank. If a child gets a marked
apple, he or she wins a prize. ‘ (a) Find the probability that two children Win a prize.
(b) Find the probability that less than two children win a prize.
(0) Find the probability that all the children win a prize. 4. (20 points) A local high school basketball player with a lifetime free throw percentage of 85% enters a com
petition. He is allowed to takes ﬁve free thrdws and wins $100 for each basket made. Let X be the random
variable that describes the players winnings. ‘ (a) What values may X take? ‘
(b) Create a table that describes the probability distribution of X (c) Find his expected winnings. Find the variance in his winnings.
5. (20 points) Let Z be a normally distributed random variable. (a) Find P(0.4O < Z). (b) Find P (0.55 > Z) (c) Find P(—2.73 < Z < —2.14). . (d) Find 2 such that P(——1.00 < Z < z) = 0.16990. 6. (15 points) A fair, sixsided die is rolled 9,000 times. Let X be the number of times the number two is rolled. (
Approximate with a normal distribution the following: (a) P(X < 1000)
(b) P (1000 < X < 8000)
(c) P (X > 8000) Please rewrite by hand and sign the honor pledge on your exam booklet: “I pledge on my honor that
I have not given or received any unauthorized assistance on this examination.” ...
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