155S5.2.notebook
February 10, 2010
MAT 155­DY1 and DY2
5.1­5.2 Random Variables
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Frequency Tables and Probability Distributions
Discrete Random Variables
Continuous Random Variables
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155S5.2.notebook
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155S5.2.notebook
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Section 5.2 Random Variables
221/6. Identify the random variable as discrete or continuous.
(a) The cost of conducting a genetics experiment
(b) The number of supermodels who ate pizza yesterday
(c) The exact life span of a kitten
Sep 16­1:36 PM
Section 5.2 Random Variables
221/6. Identify the random variable as discrete or continuous.
(d) The number of statistics professors who read a newspaper each day
(e) The weight of a feather
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155S5.2.notebook
February 10, 2010
Section 5.2 Random Variables
222/8. Determine if a probability distribution is given. If so, find the mean and standard deviation.
When groups of four children are randomly selected from a population of couples meeting certain criteria, the probability distribution for the number of girls is as given in the table.
Sep 16­1:36 PM
Section 5.2 Random Variables
222/10. Determine if a probability distribution is given. If so, find the mean and standard deviation.
For a group of four men, the probability distribution for the number x who live through the next year is as given in the table.
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155S5.2.notebook
February 10, 2010
Section 5.2 Random Variables
222/14. Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican­Americans. Refer to Table 5­1 and find the indicated probabilities.
(a) Find the probability of exactly 6 Mexican­Americans among 12 jurors. Sep 16­1:36 PM
Section 5.2 Random Variables
222/14. Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican­Americans. Refer to Table 5­1 and find the indicated probabilities.
(b) Find the probability of 6 or fewer Mexican­Americans among 12 jurors.
(c) Which probability is relevant for determining whether 6 jurors among 12 is unusually low: part (a) or part (b)?
(d) Does 6 Mexican­Americans among 12 jurors suggest that the selection process discriminates against Mexican­Americans? Why or why not?
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155S5.2.notebook
February 10, 2010
Section 5.2 Random Variables
223/16. Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican­Americans. Refer to Table 5­1 and find the probability.
(a) Find the probability that should be used for determining whether the result of 11 Mexican­Americans among 12 jurors is unusually high.
(b) Does the selection of 11 Mexican­American jurors suggest that the selection process favors Mexican­Americans? Why or why not?
Sep 16­1:36 PM
Section 5.2 Random Variables
223/18. When you give a casino $5 for a bet on the “pass line” in a casino game of dice, there is a 251/495 probability that you will lose $5 and there is a 244/495 probability that you will make a net gain of $5. What is your expected value? In the long run, how much do you lose for each dollar bet?
Solution to the problem is as follows:
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155S5.2.notebook
February 10, 2010
Section 5.2 Random Variables
223/22. Let the random variable x represent the number of girls in a family of four children. Construct a table describing the probability distribution, then find the mean and standard deviation.
Solution to the problem is as follows:
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