What is the mean of Z, the expected total number of individuals (males and females) who are colorblind?

Here is what is given:Colorblindness is any abnormality of the color vision system that causes a person to see colors differently than most people or to have difficulty distinguishing among certain colors (www.visionrx.xom).





Colorblindness is gender-based with the majority of sufferers being males.





Roughly 8% of white males have some form of colorblindness, while the incidence among white females is only 1%.





A random sample of 20 white males and 40 white females was chosen.





Let X be the number of males (out of the 20) who are colorblind.





Let Y be the number of females (out of the 40) who are colorblind.





Let Z be the total number of colorblind individuals in the sample (males and females together).





Answers:


(a) .4


(b) 1.6


(c) 2


(d) 2.7


(e) The mean of Z cannot be determined.





Hint: Express Z in terms of X and Y and then apply rules for means.

What is the mean of Z, the expected total number of individuals (males and females) who are colorblind?
The answer is (c)





Let X be a random variable with mean μx and variance σx². Let a, and b be constants.





Let W = aX + b





The mean of W, E(W) = μw is:





E(W) = E(aX + b)


= E(aX) + b


= aE(X) + b











in this case we have Z = X + Y





E(X) = 20 * 0.08 = 1.6


E(Y) = 0.4





E(Z) = 1.6 + 0.4 = 2.0
Reply:Since it affects 8% of white males (X), and 1% of white females (Y), then the average number of people (Z), both genders, that are infected will be





Z = 0.08X + 0.01Y


Z = 0.08(20) + 0.01(40)


Z = 2





I would have to say c is the answer.





Hope that helps!!!!!!
Reply:The expectation should just be the weight(probability) multiply by the amount of people.





Mean of X is : (.08*20)





Mean of Y is : (.01*40)





Mean of Z is the addition of the mean of Y and the mean of X





μ_z = μ_x + μ_y





μ_z = (.08*20) + (.01*40) = 2