Question

Antibiotic resistance occurs when disease-causing microbes become resistant to antibiotic drug therapy. Because this resistance is typically genetic and transferred to the next generation of microbes, it is a very serious public health problem. According to the CDC, 30% of gonorrhea cases tested in 2004 were resistant to the antibiotic ciprofloxacin. A physician prescribed ciprofloxacin for the treatment of 5 cases of gonorrhea during one week of 2004. Find the probability that at least 3 cases were resistant to ciprofloxacin.

Round your answer to 4 decimal places.

Answer 1

Given X~Binomial(n = 5, p = 0.30)

PMF of Binomial distribution is

We have to find the probability that at least 3 cases were resistant to ciprofloxacin.

That is we have to find P(X 3)

P(X 3) = P(X = 3) + P(X = 4) + P(X = 5)

P(X 3) = P(X = 3) + P(X = 4) + P(X = 5) = 0.1323 + 0.0284 + 0.0024 = 0.1631