White boxers are dogs that have a genetic disposition for going deaf within the

Question

White boxers are dogs that have a genetic disposition for going deaf within the first year after they are born. Suppose a litter of ten white boxer puppies contained two dogs that would eventually experience deafness. A family randomly selected two puppies from this litter to take home as family pets. (For this problem, define a success as selecting a dog that will eventually experience deafness.) Complete parts a through d below.

a. Determine the probability that none of the two puppies selected will experience deafness.

b. Determine the probability that one of the two puppies selected will experience deafness.

c. Determine the probability that all two puppies selected will experience deafness.

d. Calculate the mean and standard deviation of this distribution.

Explanation / Answer

probability that puppies will face deafness = 2/10 = 0.2

probability that puppies will not face deafness =0.8

a) p(0 puppies have deafness) = 2C0*(0.2)^0*(0.8)^2 = 0.64

B) P(1 WILL EXPERIENCE DEAFNESS) = 2C1*(0.2)^1*(0.8)^1 = 0.32

C) P(2 WILL FACE DEAFNESS) = 2C2*(0.2)^2*(0.8)^0 = 0.04

D) MEAN = E(X) = X1*P(X1)+X2*P(X2)+,,,,+XN*P(XN)

= 0*0.64+1*0.32+2*0.04 = 0.40

VAR(X) = E(X^2) + E(X)^2 = 1*0.32+4*0.04 - 0.16 = 0.32

STANDARD DEV = VAR(X)^(1/2) = 0.565

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