Chapter Test 229 Chapter Test 4 Take this test as you would take a test in class. In Exercises 1–3, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. 1. One out of every 42 tax returns for incomes over $1 million requires an audit. An auditor is examining tax returns for over $1 million. Find the probability that (a) the first return requiring an audit is the 25th return the tax auditor examines, (b) the first return requiring an audit is the first or second return the tax auditor examines, and (c) none of the first five returns the tax auditor examines require an audit. (Source: Kiplinger) 2. About 53% of U.S. full-time college students drank alcohol within a one-month period. You randomly select six U.S. full-time college students. Find the probability that the number who drank alcohol within a one-month period is (a) exactly two, (b) at least three, and (c) less than four. (Source: National Center for Biotechnology Information) 3. The mean increase in the U.S. population is about 1.5 people per minute. Find the probability that the increase in the U.S. population in any given minute is (a) exactly three people, (b) more than four, and (c) at most four people. (Source: U.S. Census Bureau) 4. Determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. (a) x 0 5 10 15 20 P1x2 0.03 0.09 0.19 0.32 0.37 (b) x 1 2 3 4 5 6 P1x2 1 20 1 10 2 5 3 10 1 5 1 25 5. The table shows the ages of students in a freshman orientation course. Age 17 18 19 20 21 22 Students 2 13 4 3 2 1 (a) Construct a probability distribution. (b) Graph the probability distribution using a histogram and describe its shape. (c) Find the mean, variance, and standard deviation of the probability distribution and interpret the results. (d) Find the probability that a randomly selected student is less than 20 years old. 6. Fifty-six percent of federal student loans are in repayment. You randomly select five student loans and determine whether they are in repayment. The random variable represents the number that are in repayment. (Source: U.S. Department of Education) (a) Construct a probability distribution. (b) Graph the probability distribution using a histogram and describe its shape. (c) Find the mean, variance, and standard deviation of the probability distribution and interpret the results.
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