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Chapter 5: Q. 53 (page 329)
Union and intersection Suppose A and B are two events such that P (A), P (B), and
P (A∪B). Find P (A∩B).
The Pis.
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Crawl before you walk (At what age do babies learn to crawl? Does it take
longer to learn in the winter, when babies are often bundled in clothes that restrict their
movement? Perhaps there might even be an association between babies’ crawling age and
the average temperature during the month they first try to crawl (around months after
birth). Data were collected from parents who brought their babies to the University of
Denver Infant Study Center to participate in one of a number of studies. Parents reported
the birth month and the age at which their child was first able to creep or crawl a distance
of feet within one minute. Information was obtained on infants. Crawling age is given in weeks, and average temperature (in degrees Fahrenheit) is
given for the month that is months after the birth month.
a. Make an appropriate graph to display the relationship between average temperature and
average crawling age. Describe what you see.
Some computer output from a least-squares regression analysis of the data is shown.
b. What is the equation of the least-squares regression line that describes the relationship
between average temperature and average crawling age? Define any variables that you
use.
c. Interpret the slope of the regression line.
d. Can we conclude that warmer temperatures months after babies are born causes them
to crawl sooner? Justify your answer.
Airport securityThe Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check prior to boarding. One such flight had passengers—in first class and in coach class. Some passengers were surprised when none of the passengers chosen for screening were seated in first class. We want to perform a simulation to estimate the probability that no first-class passengers would be chosen in a truly random selection.
a. Describe how you would use a table of random digits to carry out this simulation.
b. Perform one trial of the simulation using the random digits that follow. Copy the digits onto your paper and mark directly on or above them so that someone can follow what you did.
c. In of the trials of the simulation, none of the passengers chosen was seated in first class. Does this result provide convincing evidence that the TSA officers did not carry out a truly random selection? Explain your answer.
What is the probability that the person owns a Chevy, given that the truck has four-wheel drive?
Color-blind men About of men in the United States have some form of red-green color blindness. Suppose we randomly select one U.S. adult male at a time until we find one who is red-green color-blind. Should we be surprised if it takes us or more men? Describe how you would carry out a simulation to estimate the probability that we would have to randomly select or more U.S. adult males to find one who is red-green color blind. Do not perform the simulation.
BMI (2.2, 5.2, 5.3) Your body mass index (BMI) is your weight in kilograms divided by
the square of your height in meters. Online BMI calculators allow you to enter weight in
pounds and height in inches. High BMI is a common but controversial indicator of being
overweight or obese. A study by the National Center for Health Statistics found that the
BMI of American young women (ages 20 to 29) is approximately Normally distributed
with mean 26.8 and standard deviation 7.4.
27
a. People with BMI less than 18.5 are often classed as “underweight.” What percent of
young women are underweight by this criterion?
b. Suppose we select two American young women in this age group at random. Find the
probability that at least one of them is classified as underweight.
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