Question

According to CDC estimates, more than two million people in the United States are sickened each year with antibiotic-resistant infections, with at least 23,000 dying 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 CDC, gonorrhea has an estimated 800,000 cases occurring annually, with approximately 30% of those cases resistant to any antibiotic. Assume a physician treats 7 cases of gonorrhea during a given week. (a) What is the distribution of X, the number of these 7 cases that are resistant to any antibiotic? binomial with 7 and p 2.1 binomial with n 800,000 and p 0.30 0 binomial with n-1 and p-0.30 O binomial with 7 and p 30 O not binomial 0 binomial with n = 0.30 and p = 7 0 binomial with n = 800,000 and p 070 (b) What is the mean of X? (Enter your answer rounded to one decimal place.) mean of X- What is the standard deviation of X? (Enter your answer rounded to three decimal places.) standard deviation of X -

Answer 1

Answer Date: 31/08/2019 a) The distribution of X is binomial, the number of these 7 cases that are resistant to any antibiotic with sample size 7 and proportion is 0.30. The answer option is 3). b) The mean of the binomial distribution is, A = np = 7 x 0.30 = 2.1 The mean of the binomial distribution is 2.1).

The standard deviation of the binomial distribution is, o = Vnp(1 – p) = 70.30% (1 -0.30) = 1.212 The standard deviation of the binomial distribution is 1.212. The probability is that exactly one out of the 7 cases is resistant to any antibiotic is, p(x = 1) =,Cxp* (1-p)*** =, C (0.30)' + (1 -0.30)74 = 0.2471 The probability is that exactly one out of the 7 cases is resistant to any antibiotic is 0.2471 The probability is that at least one out of the 7 cases is resistant to any antibioticis,

First, compute the cumulative probability of O then subtracts from 1 for compute the probability is that at least one out of the 7 cases is resistant to any antibiotic. By using Excel software, find probability with the help of following steps: 1) Import the data. 2) Choose Discrete Probability Distributions from Probability in MegaStat option from Add-Ins menu. 3) Enter nunber of trials and probability of occurence in Binomial option. 4) Click Ok. Binomial distribution 7n 0.3 p cumulative X P(X) probability 0 0.08235 0.08235 1 0.24706 0.32942

From the Excel output, the cumulative probability of O is 0.0824. p(x > 1) =1-cum.prob(x = 0) = 1-0.0824 = 0.9176 The probability is that at least one out of the 7 cases is resistant to any antibiotic is 0.9176