A die is rolled 9 times and the number of times that two shows on the upper face is counted. If this
experiment is repeated many times, find the mean for the number of twos.
A) 7.5 B) 1.5 C) 2.25 D) 3
Q. 2Multiple-choice questions on a test each have 5 possible answers, one of which is correct.
Assume that you guess the answers to 5 such questions.
a. Use the multiplication rule to find the probability that the first 2 guesses are wrong and
the last 3 guesses are correct. That is, find P(WWCCC), where C denotes a correct answer
and W denotes a wrong answer.
b. Make a complete list of the different possible arrangements of 2 wrong answers and 3
correct answers, then find the probability for each entry in the list.
c. Based on the preceding results, what is the probability of getting exactly 3 correct
answers when 5 guesses are made?
Q. 3A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet
Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours.
If 40 mechanics
are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
A) 0.9589 B) 0.4276 C) 0.9608 D) 0.9756
Q. 4A game is said to be fair if the expected value for winnings is 0, that is, in the long run,
the player can expect to win 0. Consider the following game.
The game costs 1 to play
and the winnings are 5 for red, 3 for blue, 2 for yellow, and nothing for white. The
following probabilities apply. What are your expected winnings? Does the game favor the
player or the owner?
Outcome Probability
Red .02
Blue .04
Yellow .16
White .78
Q. 5When 100 engines are shipped, all of them are free of defects.
A) At least one of the engines is defective. B) All of the engines are defective.
C) At most one of the engines is defective. D) None of the engines are defective.
Q. 6A certain rare form of cancer occurs in 37 children in a million, so its probability is 0.000037. In the
city of Normalville there are 74,090,000 children.
A Poisson distribution will be used to
approximate the probability that the number of cases of the disease in Normalville children is
more than 2. Find the mean of the appropriate Poisson distribution (the mean number of cases in
groups of 74,090,000 children).
A) 27,400 B) 2740 C) 274 D) 0.000037
Q. 7On a multiple choice test with 17 questions, each question has four possible answers, one of which
is correct. For students who guess at all answers, find the mean for the number of correct answers.
A) 8.5 B) 12.8 C) 4.3 D) 5.7
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