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Chapter 5: Q. 100. (page 336)
Checking independence Suppose C and D are two events such that
and Are events C and D independent? Justify your answer.
The required answer is No
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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.
Who鈥檚 pregnant? According to the Current Population Survey (CPS), 27%
of U.S. females are older than 55. The Centers for Disease Control and Prevention (CDC) report that 6% of all U.S. females are pregnant. Suppose that these results are accurate. If we randomly select a U.S. female, is P(pregnant and over 55) =? Why or why not?
Dogs and cats In one large city, 40% of all households own a dog, 32% own a cat, and 18% own both. Suppose we randomly select a household.
a. Make a Venn diagram to display the outcomes of this chance process using events D: owns a dog, and C: owns a cat.
b. Find P.
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.
Double fault!A professional tennis player claims to get of her second serves in. In a recent match, the player missed of her first second serves. Is this a surprising result if the player鈥檚 claim is true? Assume that the player has a probability of missing each second serve. We want to carry out a simulation to estimate the probability that she would miss or more of her first second serves.
a. Describe how to use a random number generator to perform one trial of the simulation. The dot plot displays the number of second serves missed by the player out of the first second serves in simulated matches.
b. Explain what the dot at represents.
c. Use the results of the simulation to estimate the probability that the player would miss or more of her first second serves in a match.
d. Is there convincing evidence that the player misses more than of her second serves? Explain your answer.
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