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Chapter 5: Q 1. (page 246)
Why is probability theory important to statistics?
Probability theory help in predicting values and in the estimations in statistics.
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Craps. The game of craps is played by rolling two balanced dice. A first roll of a sum of 7 or 11 wins; and a first roll of a sum of 2,3 , or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is thrown. It can be shown that the probability is 0.493 that a player wins a game of craps. Suppose we consider a win by a player to be a success,
a. Identify the success probability,
b. Construct a table showing the possible win-lose results and their probabilities for three games of craps. Round each probability to three decimal places.
c. Draw a tree diagram for part (b).
d. List the outcomes in which the player wins exactly two out of three times.
e. Determine the probability of each of the outcomes in part (d). Explain why those probabilities are equal.
f. Find the probability that the player wins exactly two out of three times.
g. Without using the binomial probability formula, obtain the probability distribution of the random variable , the number of times out of three that the player wins.
h. Identify the probability distribution in part (g).
Vitamin C and Aspirin A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Bayer pills with 325 mg of aspirin. When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the Spring Valley vitamin C claim or rejection of the Bayer aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin?
Interpret each of the following probability statements, using the frequentist interpretation of probability.
(a). The probability is 0.487 that a newborn baby will be a girl.
(b). The probability of a single ticket winning a prize in the Powerball lottery is 0.031.
Suppose that C and D are mutually exclusive events such that and Determine .
Dice. Refer to exercise 5.53.
a Are events A and B mutually exclusive?
b Are events B and C mutually exclusive?
c Are events A, C and D mutually exclusive?
d Are there three mutually exclusive events among A, B, C and D? four?
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