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Chapter 5: Q 67. (page 332)
Tall people and basketball players Select an adult at random. Define events T: person is over feet tall, and
B: person is a professional basketball player. Rank the following probabilities from smallest to largest. Justify your answer.
The correct order is
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Smartphone addiction? A media report claims that of U.S. teens with smartphones feel addicted to their devices. A skeptical researcher believes that this figure is too high. She decides to test the claim by taking a random sample of U.S. teens who have smartphones. Only of the teens in the sample feel addicted to their devices. Does this result give convincing evidence that the media report’s claim is too high? To find out, we want to perform a simulation to estimate the probability of getting or fewer teens who feel addicted to their devices in a random sample of size from a very large population of teens with smartphones in which 50% feel addicted to their devices.
Let = feels addicted and = doesn’t feel addicted. Use a random number generator to produce random integers from to . Record the number of ’s in the simulated random sample. Repeat this process many, many times. Find the percent of trials on which the number of ’s was or less.
Four-sided dice A four-sided die is a pyramid whose four faces are labeled
with the numbers and(see image). Imagine rolling two fair, four-sided dice and
recording the number that is showing at the base of each pyramid. For instance, you would
record a if the die landed as shown in the figure.
a. Give a probability model for this chance process.
b. Define event A as getting a sum of . Find P(A).
A basketball player claims to make of her shots from the field. We want to simulate the player taking sets of shots, assuming that her claim is true.
To simulate the number of makes in shot attempts, you would perform the simulation as follows:
a. Use random one-digit numbers, where are a make and are a miss.
b. Use random two-digit numbers, where are a make and are a miss.
c. Use random two-digit numbers, where are a make and are a miss.
d. Use random one-digit numbers, where is a make and are a miss.
e. Use random two-digit numbers, where are a make and are a miss.
Superpowers A random sample of children from England and the United States who completed a survey in a recent year was selected. Each student’s country of origin was recorded along with which superpower they would most like to have: the ability to fly, ability to freeze time, invisibility, superstrength, or telepathy (ability to read minds). The data are summarized in the two-way table.
Suppose we randomly select one of these students. Define events E: England, T: telepathy,
and S: superstrength.
a. Find . Interpret this value in context.
b. Given that the student did not choose superstrength, what’s the probability that this child is from England is ? Write your answer as a probability statement using correct symbols for the events.
When did you leave? The National Household Travel Survey gathers data on the time of day when people begin a trip in their car or other vehicle. Choose a trip at random and record the time at which the trip started. Here is an assignment of probabilities for the outcomes :
a. What probability should replace “?” in the table? Why?
b. Find the probability that the chosen trip did not begin between A.M. and P.M.
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