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For each situation, identify the sample size \(n\), the probability of a success \(p\), and the number of success \(x\). When asked for the probability, state the answer in the form \(b(n, p, x)\). There is no need to give the numerical value of the probability. Assume the conditions for a binomial experiment are satisfied. Since the Surgeon General's Report on Smoking and Health in 1964 linked smoking to adverse health effects, the rate of smoking the United States have been falling. According to the Centers for Disease Control and Prevention in 2016, \(15 \%\) of U.S. adults smoked cigarettes (down from \(42 \%\) in the \(1960 \mathrm{~s}\) ). a. If 30 Americans are randomly selected, what is the probability that exactly 10 are smokers? b. If 30 Americans are randomly selected, what is the probability that exactly 25 are not smokers?

According to the American Veterinary Medical Association, \(30 \%\) of Americans own a cat. a. Find the probability that exactly 2 out of 8 randomly selected Americans own a cat. b. In a random sample of 8 Americans, find the probability that more than 3 own a cat.

According to a survey conducted by OnePoll, a marketing research company, \(10 \%\) of Americans have never traveled outside their home state. Assume this percentage is accurate. Suppose a random sample of 80 Americans is taken. a. Find the probability that more than 12 have never travelled outside their home state. b. Find the probability that at least 12 have never travelled outside their home state. c. Find the probability that at most 12 have never travelled outside their home state.

According to the Centers of Disease Control and Prevention, \(52 \%\) of U.S. households had no landline and only had cell phone service. Suppose a random sample of 40 U.S. households is taken. a. Find the probability that exactly 20 the households sampled only have cell phone service. b. Find the probability that fewer than 20 households only have cell phone service. c. Find the probability that at most 20 households only have cell phone service. d. Find the probability that between 20 and 23 households only have cell phone service.

According to the Centers of Disease Control and Prevention, \(44 \%\) of U.S. households still had landline phone service. Suppose a random sample of 60 U.S. households is taken. a. Find the probability that exactly 25 of the households sampled still have a landline. b. Find the probability that more than 25 households still have a landline. c. Find the probability that at least 25 households still have a landline. d. Find the probability that between 20 and 25 households still have a landline.

The use of drones, aircraft without onboard human pilots, is becoming more prevalent in the United States. According to a 2017 Pew Research Center report, \(59 \%\) of American had seen a drone in action. Suppose 50 Americans are randomly selected. a. What is the probability that at least 25 had seen a drone? b. What is the probability that more than 30 had seen a drone? c. What is the probability that between 30 and 35 had seen a drone? d. What is the probability that more than 30 had not seen a drone?

In Toronto, Canada, \(55 \%\) of people pass the drivers' road test. Suppose that every day, 100 people independently take the test. a. What is the number of people who are expected to pass? b. What is the standard deviation for the number expected to pass? c. After a great many days, according to the Empirical Rule, on about \(95 \%\) of these days, the number of people passing will be as low as and as high as (Hint: Find two standard deviations below and two standard deviations above the mean.) d. If you found that on one day, 85 out of 100 passed the test, would you consider this to be a very high number?

Toronto drivers have been going to small towns in Ontario (Canada) to take the drivers' road test, rather than taking the test in Toronto, because the pass rate in the small towns is \(90 \%\), which is much higher than the pass rate in Toronto. Suppose that every day, 100 people independently take the test in one of these small towns. a. What is the number of people who are expected to pass? b. What is the standard deviation for the number expected to pass? c. After a great many days, according to the Empirical Rule, on about \(95 \%\) of these days the number of people passing the test will be as low as and as high as d. If you found that on one day, 89 out of 100 passed the test, would you consider this to be a very high number?

Determine whether each of the following variables would best be modeled as continuous or discrete: a. Number of girls in a family b. Height of a tree c. Commute time d. Concert attendance

Medical school graduates who want to become doctors must pass the U.S. Medical Licensing Exam (USMLE). Scores on this exam are approximately Normal with a mean of 225 and a standard deviation of \(15 .\) Use the Empirical Rule to answer these questions. a. Roughly what percentage of USMLE scores will be between 210 and 240 ? b. Roughly what percentage of USMLE scores will be below 210 ? c. Roughly what percentage of USMLE scores will be above 255 ?