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Chapter 5: Q2 (page 195)
Is the random variable given in the accompanying table discreteor continuous? Explain.
Number of Girls x | P(x) |
0 | 0.063 |
1 | 0.25 |
2 | 0.375 |
3 | 0.25 |
4 | 0.063 |
The variable x is a discrete random variable.
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Expected Value in Virginia’s Pick 3 Game In Virginia’s Pick 3 lottery game, you can pay \(1 to select a three-digit number from 000 through 999. If you select the same sequence of three digits that are drawn, you win and collect \)500.
a. How many different selections are possible?
b. What is the probability of winning?
c. If you win, what is your net profit?
d. Find the expected value.
e. If you bet \(1 in Virginia’s Pick 4 game, the expected value is -50¢. Which bet is better in the sense of a producing a higher expected value: A \)1 bet in the Virginia Pick 3 game or a $1 bet in the Virginia Pick 4 game?
In Exercises 7–14, determine whether a probability
distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
When betting on the pass line in the dice game of craps at the Mohegan Sun casino in Connecticut, the table lists the probabilities for the number of bets that must be placed in order to have a win.
x | P(x) |
1 | 0.493 |
2 | 0.25 |
3 | 0.127 |
4 | 0.064 |
In Exercises 7–14, determine whether a probability
distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Five males with an X-linked genetic disorder have one child each. The random variable xis the number of children among the five who inherit the X-linked genetic disorder.
x | P(x) |
0 | 0.031 |
1 | 0.156 |
2 | 0.313 |
3 | 0.313 |
4 | 0.156 |
5 | 0.031 |
Ultimate Binomial Exercises! Exercises 37–40 involve finding binomial probabilities, finding parameters, and determining whether values are significantly high or low by using the range rule of thumb and probabilities.
M&Ms Data Set 27 “M&M Weights” in Appendix B includes data from 100 M&M candies, and 19 of them are green. Mars, Inc. claims that 16% of its plain M&M candies are green. For the following, assume that the claim of 16% is true, and assume that a sample consists of 100 M&Ms.
a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the result of 19 green M&Ms significantly high?
b. Find the probability of exactly 19 green M&Ms.
c. Find the probability of 19 or more green M&Ms.
d. Which probability is relevant for determining whether the result of 19 green M&Ms is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 19 green M&Ms significantly high?
e. What do the results suggest about the 16% claim by Mars, Inc.?
Notation of 0+ Using the same survey from Exercise 3, the probability of randomly selecting 30 of the 1009 consumers and getting exactly 24 who are comfortable with the drones is represented as 0+. What does 0+ indicate? Does 0+ indicate that it is impossible to get exactly 24 consumers who are comfortable with the drones?
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