In: Statistics and Probability
According to the CDC, certain microbes are becoming resistant to antibiotic drug therapy and therefore pose a serious public health risk. The CDC lists antibiotic-resistant gonorrhea as one of most serious of these kinds of infections. 30% of all gonorrhea infections are antibiotic-resistant. Suppose that 15 individuals are receiving treatment for gonorrhea at a particular clinic. Use what you know about the binomial distribution to answer the following questions.
a. What is the probability that exactly 5 of the 15 individuals have antibiotic-resistant gonorrhea?
b. What is the probability that 5 or fewer of these individuals have antibiotic-resistant gonorrhea?
c. What is the probability that more than 7 of these individuals have antibiotic-resistant gonorrhea?
d. What is the expected number of individuals that have antibiotic-resistant gonorrhea?
e. What is the standard deviation of the number of individuals that have antibiotic-resistant gonorrhea?