Chapter 4: Q.3 (page 282)
Short Answer
The necessary probability is .
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Chapter 4: Q.3 (page 282)
The necessary probability is .
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The World Bank records the prevalence of HIV in countries around the world. According to their data, 鈥淧revalence of HIV refers to the percentage of people ages 15 to 49 who are infected with HIV.鈥漑1] In South Africa, the prevalence of HIV is 17.3%. Let X = the number of people you test until you find a person infected with HIV.
a. Sketch a graph of the distribution of the discrete random variable X.
b. What is the probability that you must test 30 people to find one with HIV?
c. What is the probability that you must ask ten people?
d. Find the
(i) mean and
(ii) standard deviation of the distribution of X.
Approximately of students at a local high school participate in after-school sports all four years of high school. A group of seniors is randomly chosen. Of interest is the number that participated in after-school sports all four years of
high school.
a. In words, define the random variable .
b. List the values that may take on.
c. Give the distribution of
d. How many seniors are expected to have participated in after-school sports all four years of high school?
e. Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all
four years of high school.
f. Based on numerical values, is it more likely that four or that five of the seniors participated in after-school sports
all four years of high school? Justify your answer numerically.
Identify the mistake in the probability distribution table.
What values does X take on?
Suppose you play a game with a spinner. You play each game by spinning the spinner once. P(red) = , P(blue) = , and P(green) = . If you land on red, you pay . If you land on blue, you don't pay or win anything. If you land on green, you win . Complete the following expected value table.
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