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Chapter 4: Q.67 (page 287)
Is it likely that there will be no teens killed from motor vehicle injuries on any given day in the U.S? Justify your answer numerically
No, it isn't likely that there will be no teens killed from motor vehicle injuries on any given day in theU.S.
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It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. What is the probability that we must survey just one or two residents until we find a California resident who does not have adequate earthquake supplies?
e. What is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies?
f. How many California residents do you expect to need to survey until you find a California resident who does not have adequate earthquake supplies?
g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?
A theater group holds a fund-raiser. It sells 100 raffle tickets for \(5 apiece. Suppose you purchase four tickets. The prize is two passes to a Broadway show, worth a total of \)150.
a. What are you interested in here?
b. In words, define the random variable X.
c. List the values that X may take on.
d. Construct a PDF.
e. If this fund-raiser is repeated often and you always purchase four tickets, what would be your expected average winnings per raffle?
A group of Martial Arts students is planning on participating in an upcoming demonstration. Six are students of Tae Kwon Do; seven are students of Shotokan Karate. Suppose that eight students are randomly picked to be in the first demonstration. We are interested in the number of Shotokan Karate students in that first demonstration.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. How many Shotokan Karate students do we expect to be in that first demonstration?
Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. One week is selected at random. What values does X take on?
According to a Gallup poll, 60% of American adults prefer saving over spending. Let X = the number of American adults out of a random sample of 50 who prefer saving to spending.
a. What is the probability distribution for X?
b. Use your calculator to find the following probabilities:
i. the probability that 25 adults in the sample prefer saving over spending
ii. the probability that at most 20 adults prefer saving
iii. the probability that more than 30 adults prefer saving
c. Using the formulas, calculate the
(i) mean and
(ii) standard deviation of X.
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