Each day a large animal clinic are testing 7 horses for a common disease. The pr

Question

Each day a large animal clinic are testing 7 horses for a common disease. The probability of a horse having symptoms for the disease is 15%. If a horse has symptoms for the disease, treatment is given 95% of the time. If a horse is not having symptoms for the disease, treatment is given 7% of the time.

(A) What is the probability that treatment is given to at least one horse each day?

(B) The money the clinic gets for treating a horse is 600$. What is the expected daily revenue that the clinic earns from treating horses? What is the variance of the daily revenue that the clinic earns from treating horses?

Explanation / Answer

A)P(treatment) =P(have disease and treatment +not have disease and treatment)=0.15*0.95+(1-0.15)*0.07=0.202

threfore probability that treatment is given to at least one horse each day =1-P(treatment given to none of 7)

=(1-0.202)7=0.7939

B)let X is number of horses treated dailiy and revenue is Y

hence Y=600X

expected daily revenue =600*E(X) =600*np =600*7*0.7939=$3334.495

variance =6002*Var(X)=360000*np(1-p) =360000*7*0.7939*(1-0.7939)=412288.8

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