Question

Wisconsin, Stout - STAT 130 900C-Falt19WU > Activities and Due Dates > HW (14) < Assignment Score: 920/1500 Resources [ Give Up? Check Answer < Question 15 of 15 > 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 discase-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 three infections considered most serious by the CDC, gonorrhea has an estimated 800,000 cases occurring annually, with approximately 30% of those cases resistant to any antibiotic. Assume a physician treats 9 cases of gonorrhea during a given week. (a) What is the distribution of X, the number of these 9 cases that are resistant to any antibiotic? O binomial with n = 0.30 and p = 9 O not binomial O binomial with n = 800,000 and p = 0.30 O binomial with n=9 and p = 2.7 Question Source: Moore, The Basic Practice of Statistics, Be Publisher W. Fre A 9:46 PM 11/9/2019 Et Poule DOM 9 X

Answer 1

a)

Binomial with n=9 and p=0.3

Note that the value of p is lies between o to 1

b)

Mean of X is

np=9*0.3=2.7

Standard deviation of X is

√(npq) =√(9*0.3*0.7)=1.375

Where q=1-p

C)

P(X=1)=0.1556

P(X>=1)=1-P(X<1)=1-P(X=0)=0.9596

According to coc estimates, more than two million people in us. Gre stickened each year with antibiotic - resistant infection with atleast 23,000 dying as result. Antibiotic resistance occurs when disease -causing microbes become resistant to antibiotic drug theerapy. Because this resistance is typically genetic and transfered to the next generations of microbes. It is very serious public health problem of the three infection considered most serious by the COC, gonorrhea has estimated 300,000 cases occuring annulally, with approximately 30% of those case resistant to any antibiotic. Assume a physican I treats 9 cases of gonorrhea during a given week. is B 7 The distribution of x Let X be the number of these 9 cases that are resistant to ony any antibiotic ii Here nag with probobility 0.30 Cappooximo lely 30% of those cases resistant p=0.30 to any antibiotic $ 30% means 0-30 retribution of x is Binomial with n=9&p=0:20 of of binomio) disth is P[x=] = " pre ci-phase 3-0,1,27mn P[X=~) = 160.303 CO-7.9.-2 осе 4 and it theor otical mean and voriance & standard deviatron meon = np , variance - npq , standord deviation - hea where 4- p The mean of x is np= 9X 0.30 = 2.7 The standard deviation of x is vnpa = 59X0:3X0.7 = V1-89 = 1-3747 = 1-375 © The probability that exactly one out of the g cases 15 resis tont to any antibiotic? P(X=0 = 2, t32' to: 3 x 3 x 18 _ 0.1554 20-1556 what is the probability that atleast one case resistant to anu 5 antibiotic ic P(x | = |- Px & D = EN - Pxze] PCX70= 1- P(X=0) - 1-9 0.20 0.79 .10.7°= 0.9596