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14.24 Antibiotic Resistance. According to CDC estimates, at least 2.8 million people in the United States are sickened each year with antibiotic-resistant infections, and at least 35,000 die as a result. Antibiotic resistance occurs when disease-causing microbes become resistant to antibiotic drug therapy. Because this resistance is typically genetic and transferred to the next generations of microbes, it is a very serious public health problem. Of the infections considered most serious by the CDC, gonorrhea has an estimated 1.14 million new cases occurring annually, and approximately 50% of those cases are resistant to any antibiotic. A public health clinic in California sees eight patients with gonorrhea in a given week. a. What is the distribution of X, the number of these eight cases that are resistant to any antibiotic? b. What are the mean and standard deviation of X? c. Find the probability that exactly one of the cases is resistant to any antibiotic. What is the probability that at least one case is resistant to any antibiotic? (Hint: It is easier to first find the probability that exactly zero of the eight cases were resistant.)

14.24 Antibiotic Resistance. According to CDC estimates, at least 2.8 million people in the United States are sickened each year with antibiotic-resistant infections, and at least 35,000 die as a result. Antibiotic resistance occurs when disease-causing microbes become resistant to antibiotic drug therapy. Because this resistance is typically genetic and transferred to the next generations of microbes, it is a very serious public health problem. Of the infections considered most serious by the CDC, gonorrhea has an estimated 1.14 million new cases occurring annually, and approximately 50% of those cases are resistant to any antibiotic. A public health clinic in California sees eight patients with gonorrhea in a given week. a. What is the distribution of X, the number of these eight cases that are resistant to any antibiotic? b. What are the mean and standard deviation of X? c. Find the probability that exactly one of the cases is resistant to any antibiotic. What is the probability that at least one case is resistant to any antibiotic? (Hint: It is easier to first find the probability that exactly zero of the eight cases were resistant.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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14.24 Antibiotic Resistance. According to CDC estimates, at least 2.8 million people in the United States are sickened each year with antibiotic-resistant infections, and at least 35,000 die as a result. Antibiotic resistance occurs when disease-causing microbes become resistant to antibiotic drug therapy. Because this resistance is typically genetic and transferred to the next generations of microbes, it is a very serious public health problem. Of the infections considered most serious by the CDC, gonorrhea has an estimated 1.14 million new cases occurring annually, and approximately 50% of those cases are resistant to any antibiotic. A public health clinic in California sees eight patients with gonorrhea in a given week. a. What is the distribution of X, the number of these eight cases that are resistant to any antibiotic? b. What are the mean and standard deviation of X? c. Find the probability that exactly one of the cases is resistant to any antibiotic. What is the probability that at least one case is resistant to any antibiotic? (Hint: It is easier to first find the probability that exactly zero of the eight cases were resistant.)
Transcribed Image Text:14.24 Antibiotic Resistance. According to CDC estimates, at least 2.8 million people in the United States are sickened each year with antibiotic-resistant infections, and at least 35,000 die as a result. Antibiotic resistance occurs when disease-causing microbes become resistant to antibiotic drug therapy. Because this resistance is typically genetic and transferred to the next generations of microbes, it is a very serious public health problem. Of the infections considered most serious by the CDC, gonorrhea has an estimated 1.14 million new cases occurring annually, and approximately 50% of those cases are resistant to any antibiotic. A public health clinic in California sees eight patients with gonorrhea in a given week. a. What is the distribution of X, the number of these eight cases that are resistant to any antibiotic? b. What are the mean and standard deviation of X? c. Find the probability that exactly one of the cases is resistant to any antibiotic. What is the probability that at least one case is resistant to any antibiotic? (Hint: It is easier to first find the probability that exactly zero of the eight cases were resistant.)
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