BackLong Life? In a poll conducted by Genworth Financial, a random sample of adults was asked, “What age would you like to live to?” The results of the survey are given in the table.
a. Construct a probability model of the data.
Gestation Period versus Weight The following data represent the birth weights (in grams) of babies born in 2017, along with the period of gestation.
b. What is the probability that a randomly selected baby born in 2017 weighed between 3000 and 3999 grams?
Gestation Period versus Weight The following data represent the birth weights (in grams) of babies born in 2017, along with the period of gestation.
e. What is the probability that a randomly selected baby born in 2017 weighed less than 1000 grams and was postterm? Is this event possible?
Who Do You Trust?
According to the National Constitution Center, 18% of Americans trust organized religion.
c. In a random sample of three Americans, all three indicated they trust organized religion. Is this result surprising?
Pick 4 The Illinois Lottery’s PICK 4 game is similar to PICK 3, except a player must match a sequence of four repeatable numbers, ranging from 0 to 9, in exact order (for example, 5–8–5–1). With a single ticket, what is the probability of matching the four winning numbers?
Arizona’s Pick 5 In one of Arizona’s lotteries, balls are numbered 1–35. Five balls are selected randomly, without replacement. The order in which the balls are selected does not matter. To win, your numbers must match the five selected. Determine your probability of winning Arizona’s Pick 5 with one ticket.
Packaging Error
Because of a mistake in packaging, a case of 12 bottles of red wine contained five Merlot and seven Cabernet, each without labels. All the bottles look identical and any has an equal chance of being chosen. Three bottles are selected at random.
b. What is the probability that exactly two are Merlot?
Simulation
Use a graphing calculator or statistical software to simulate the game of roulette, using an integer distribution for the numbers 1 through 38. Repeat the simulation 100 times. Let the number 37 represent 0 and the number 38 represent 00. Use the results of the simulation to answer the following questions.
b. What is the probability that the ball lands either in the slot marked 0 or in the one marked 00?
Flipping a Coin What is the probability of obtaining five heads in a row when flipping a fair coin? Interpret this probability.
"Derivatives
In finance, a derivative is a financial asset whose value is determined (derived) from a bundle of various assets, such as mortgages. Suppose a randomly selected mortgage has a probability of 0.01 of default.
d. In part (b), we made the assumption that the likelihood of default is independent. Do you believe this is a reasonable assumption? Explain."
"Driver Fatalities The following data represent the number of drivers involved in a fatal crash in 2016 in various light and weather conditions.
c. Is the dark (without light) more dangerous in normal weather or in rain? Explain."
"Putting It Together: Success Sequence
Is there a ""path"" to success? Brookings scholars Ron Haskins and Isabel Sawhill suggest the path to success is: education, followed by work, followed by marriage, followed by children. Sociologists Wendy Wang and W. Bradford Wilcox tracked a cohort of young millennial adults from their teenage years to early adulthood (ages 28 to 34) and recorded information about their education, marital status, child-rearing, and income.
a. Why is this a cohort study?
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"Randomly Playing Songs
Suppose a Spotify playlist you just created has 13 tracks. After listening to the playlist, you decide that you like 5 of the songs. The random feature on Spotify is set up to play each of the 13 songs once in a random order. Find the probability that among the first 4 songs played:
b. You like 3 of them;
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"Simulating Election Results
Suppose that polls indicate a candidate in a local school board election has the support of 52% of voters.
a. Explain how you could use the integers from 1 to 100 to simulate votes.
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What method of assigning probabilities to a simple event uses relative frequencies?