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Chapter 5: Q. 47 (page 328)
Dogs and cats In one large city, of all households own a dog, own a cat, and own both. Suppose we randomly select a household. What鈥檚 the probability that the household owns a dog or a cat?
The likelihood that the household owns either a dog or a cat is
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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鈥� 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.
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 鈥渦nderweight.鈥� 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.
Liar, liar! Sometimes police use a lie detector test to help determine whether a suspect is
telling the truth. A lie detector test isn鈥檛 foolproof鈥攕ometimes it suggests that a person is
lying when he or she is actually telling the truth (a 鈥渇alse positive鈥�). Other times, the test
says that the suspect is being truthful when he or she is actually lying (a 鈥渇alse negative鈥�).
For one brand of lie detector, the probability of a false positive is 0.08.
a. Explain what this probability means.
b. Which is a more serious error in this case: a false positive or a false negative? Justify
your answer.
The partially complete table that follows shows the distribution of scores on the AP庐
Statistics exam for a class of students.
Select a student from this class at random. If the student earned a score of 3 or higher
on the AP庐 Statistics exam, what is the probability that the student scored a 5?
In an effort to find the source of an outbreak of food poisoning at a conference, a team of medical detectives carried out a study. They examined all 50 people who had food poisoning and a random sample of 200 people attending the conference who didn鈥檛 get food poisoning. The detectives found that 40% of the people with food poisoning went to a cocktail party on the second night of the conference, while only 10% of the people in the random sample attended the same party. Which of the following statements is appropriate for describing the 40% of people who went to the party? (Let F = got food poisoning and A = attended party.)
a. P(F|A) = 0.40
b. P(A|FC) = 0.40
c. P(F|AC) = 0.40
d. P(AC|F) = 0.40
e. P(A|F) = 0.40
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