Homework for chapter 4
Due date: 11:30 am (shanghai time), 2021/10/8
Part I: Multiple-choice questions. Each question has only one correct answer.
1. Which of the following random variables is not discrete?
a. The score you received on the SAT.
b. The number of violent crimes committed per month in your community.
c. The amount of carbon monoxide produced per gallon of unleaded gas.
d. The number of bald eagles in the country.
2. The number of tickets, X, sold for a concert is of interest to the box office manager. What
values can x assume?
a. X = 0,1,2, …
b. X ≥ 0
c. X ≥ 1
d. X = 1,2, 3, …
3. A discrete random variable X can assume five possible
values, 17, 18, 19, 20, and 21. The following histogram
shows the likelihood of each value. Which of the following
is not true?
a. P (20) = 0.25
b. P (19 or 21) = 0.5
c. P (X < 20) = 0.75
d. P (X ≥ 20) = 0.5
4. Consider the following binomial variable X. Please graph its probability distribution.
5. Suppose X is a binomial random variable with p=0.5 and n=15. Would it be appropriate to
approximate the probability distribution of X with a normal distribution?
a. No, because μ±3σ lies within the boundaries of 0 and 15.
b. No, because μ±3σ lies outside the boundaries of 0 and 15.
c. Yes, because μ±3σ lies within the boundaries of 0 and 15.
d. Yes, because μ±3σ lies outside the boundaries of 0 and 15.
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Part II: Find solutions for the following problems. (For short-answer and calculated
questions, please round to 2 or 3 decimal places as needed. You will be scored on the
correctness of your methods as well as on the accuracy and completeness of your results
and explanations. So, please show all your work.)
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a. For random samples of 100 card users, what is the expected number of
customers who carry Visa? Discover?
b. Please use a normal approximation to find the probability that half or more
of the sample of card users carry Visa? American Express?
c. Justify the use of the normal approximation to the binomial in answering the
question in part c.
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