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Chapter 4: Q19 (page 143)
In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.
Square Peg Sydney Smith wrote in “On the Conduct of the Understanding” that it is impossible to fit a square peg in a round hole.
The probability of fitting a square peg in a round hole is 0.
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In Exercises 9–20, use the data in the following table, which lists drive-thru order accuracy at popular fast food chains (data from a QSR Drive-Thru Study). Assume that orders are randomly selected from those included in the table.
McDonald’s | Burger King | Wendy’s | Taco Bell | |
Order Accurate | 329 | 264 | 249 | 145 |
OrderNotAccurate | 33 | 54 | 31 | 13 |
Fast Food Drive-Thru Accuracy If two orders are selected, find the probability that they are both accurate.
a. Assume that the selections are made with replacement. Are the events independent?
b. Assume that the selections are made without replacement. Are the events independent?
In Exercises 29 and 30, find the probabilities and indicate when the “5% guideline for cumbersome calculations” is used.
Medical Helicopters In the same study cited in the preceding exercise, among the 47,637 patients transported by helicopter, 188 of them left the treatment center against medical advice, and the other 47,449 did not leave against medical advice. If 40 of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left the treatment center against medical advice?
In Exercises 25–32, find the probability and answer the questions. YSORT Gender Selection MicroSort’s YSORT gender selection technique is designed to increase the likelihood that a baby will be a boy. At one point before clinical trials of the YSORT gender selection technique were discontinued, 291 births consisted of 239 baby boys and 52 baby girls (based on data from the Genetics & IVF Institute). Based on these results, what is the probability of a boy born to a couple using MicroSort’s YSORT method? Does it appear that the technique is effective in increasing the likelihood that a baby will be a boy?
Births Example 2 in this section includes the sample space for genders from three births. Identify the sample space for the genders from two births.
Odds. In Exercises 41–44, answer the given questions that involve odds.
Relative Risk and Odds Ratio In a clinical trial of 2103 subjects treated with Nasonex, 26 reported headaches. In a control group of 1671 subjects given a placebo, 22 reported headaches. Denoting the proportion of headaches in the treatment group by and denoting the proportion of headaches in the control (placebo) group by role="math" localid="1644405830274" , the relative risk is . The relative risk is a measure of the strength of the effect of the Nasonex treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control (placebo) group, found by evaluating the following:
The relative risk and odds ratios are commonly used in medicine and epidemiological studies. Find the relative risk and odds ratio for the headache data. What do the results suggest about the risk of a headache from the Nasonex treatment?
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