Antibiotic resistance occurs when diseasecausing microbes be

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, 8% of gonorrhea cases tested in 2004 were resistant to the antibiotic ciprofloxacin. A physician prescribed ciprofloxacin for the treatment of 15 cases of gonorrhea during one week in 2004.

(a) What is the distribution of the cases resistant to ciprofloxacin?
with n = and p = (decimal)

(b) What is the probability that exactly 1 out of the 15 cases were resistant to ciprofloxacin?
(Use 3 decimal places.)

(c) What is that probability for exactly 2 out of 15?
(Use 3 decimal places.)

(d) What is the probability that 1 or more out of the 15 were resistant to ciprofloxacin? (Hint: It is easier to first find the probability that exactly 0 of the 15 cases were resistant.)
(Use 3 decimal places.)

(e) What is the mean number of gonorrhea cases that are resistant to the antibiotic ciprofloxacin out of 15 cases?

?= (Use 2 decimal places.)

(f) What is the standard deviation ? of the count of antibiotic-resistant cases?

? = (Use 3 decimal places.)

Solution

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, 6% of gonorrhea cases tested in 2004 were resistant to the antibiotic ciprofloxacin. A physician prescribed ciprofloxacin for the treatment of 10 cases of gonorrhea during one week in 2004.

with n = 10

and p = 0.06     (decimal)

(b) What is the probability that exactly 1 out of the 10 cases were resistant to ciprofloxacin? (Use 3 decimal places.)

P(X=x) = (_nC_x) p^x (1-p)^n-x   

P(X=1) = (₁₀C₁) 0.06¹ (1-0.06)^10-1   

P(X = 1) = 0.344

(c) What is that probability for exactly 2 out of 10? (Use 3 decimal places.)

P(X=2) = (₁₀C₂) 0.06² (1-0.06)^10-2   

P(X = 1) = 0.099

(d) What is the probability that 1 or more out of the 10 were resistant to ciprofloxacin? (Hint: It is easier to first find the probability that exactly 0 of the 10 cases were resistant.) (Use 3 decimal places.)

P( x>=1) =   1 - P( x=0) = 1-0.539 =0.461

(e) What is the mean number of gonorrhea cases that are resistant to the antibiotic ciprofloxacin out of 10 cases? ?= (Use 2 decimal places.)

Mean =n*p=10*0.06 =0.60