Question

Twelve reindeer at the Bronx zoo during a winter Christmas festival are diagnosed with West Nile Virus. The veterinarian believes the mortality rate for reindeer infected with West Nile Virus is 30% if the disease is left untreated, but can be reduced under treatment to 20%.

a. What is the expected value for the number of reindeer that survive without treatment?

b. What is the expected value for the number of reindeer that survive with treatment?

c. What is the probability less than 5 reindeer survive without treatment?

d. What is the probability less than 5 reindeer survive with treatment?

Answer 1

P(mortality without treatment)=0.3, this imply P(survival without treatment)=1-P(mortality without treatment)=1-0.3=0.7

P(mortality with treatment)=0.2, this imply P(survival with treatment)=1-P(survival with treatment)=1-0.2=0.8

here sample size=n=12

(a)expected value for the number of reindeer that survive without treatment=n*P(survival without treatment)=12*0.7=8.4

(b)expected value for the number of reindeer that survive with treatment=n*P(survival with treatment)=12*0.8=9.6

(c) answer=0.0095

here we use binomial distribution with parameter n=12 and p=0.7 and fpr

Binomial distribution ,P(X=r)=ⁿC_rp^r(1-p)^n-r  

probability less than 5 reindeer survive without treatment=P(X<5)=P(X<=4)=0.0095

( using ms-excel=BINOMDIST(4,12,0.7,1))

(d) answer=0.0006

here we use binomial distribution with parameter n=12 and p=0.8 and fpr

Binomial distribution ,P(X=r)=ⁿC_rp^r(1-p)^n-r  

probability less than 5 reindeer survive without treatment=P(X<5)=P(X<=4)=0.0006

( using ms-excel=BINOMDIST(4,12,0.8,1))