Chapter 5: Q5 (page 220)
Using the same SAT questions described in Exercise 2, is 8 a significantly low number of correct answers for someone making random guesses?
8 is a significantly low number of correct answers.
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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 |
Groups of people aged 15–65 are randomly selected and arranged in groups of six. The random variable xis the number in the group who say that their family and / or partner contribute most to their happiness (based on a Coca-Cola survey). The accompanying table lists
the values of xalong with their corresponding probabilities. Does the table describe a probability distribution? If so, find the mean and standard deviation.
x | P(x) |
0 | 0+ |
1 | 0.003 |
2 | 0.025 |
3 | 0.111 |
4 | 0.279 |
5 | 0.373 |
6 | 0.208 |
In Exercises 5 and 6, refer to the given values, then identify which of the following is most appropriate:discrete randomvariable, continuous random variable, ornot a random variable.
a. Exact weights of the next 100 babies born in the United States
b. Responses to the survey question “Which political party do you prefer?”
c. Numbers of spins of roulette wheels required to get the number 7
d. Exact foot lengths of humans
e. Shoe sizes (such as 8 or 8½) of humans
Identifying Binomial Distributions. In Exercises 5–12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.
Surveying Senators The Senate members of the 113th Congress include 80 males and 20 females. Forty different senators are randomly selected without replacement, and the gender of each selected senator is recorded.
Expected Value for Life Insurance There is a 0.9986 probability that a randomly selected 30-year-old male lives through the year (based on data from the U.S. Department of Health and Human Services). A Fidelity life insurance company charges \(161 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out \)100,000 as a death benefit.
a. From the perspective of the 30-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
b. If a 30-year-old male purchases the policy, what is his expected value?
c. Can the insurance company expect to make a profit from many such policies? Why?
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