Answer:
a. X is a binomial random variable with n = 50 and p = 0.04
b. Y is a binomial random variable with n = 40 and p = 0.015
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
X: the number of US residents (out of 50) with blood type AB.
Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States
This means that ![p = 0.04, n = 50](https://tex.z-dn.net/?f=p%20%3D%200.04%2C%20n%20%3D%2050)
Y: the number of Australians (out of 40) with blood type AB.
In Australia, only 1.5% of the population has blood type AB.
This means that ![p = 0.015, n = 40](https://tex.z-dn.net/?f=p%20%3D%200.015%2C%20n%20%3D%2040)
Z: the total number of individuals (out of 90) with blood type AB.
Here
![n = 90, p = 0.04*\frac{50}{90} + 0.015*\frac{40}{90} = 0.0289](https://tex.z-dn.net/?f=n%20%3D%2090%2C%20p%20%3D%200.04%2A%5Cfrac%7B50%7D%7B90%7D%20%2B%200.015%2A%5Cfrac%7B40%7D%7B90%7D%20%3D%200.0289)
Which of the following is true about the random variables X, Y, and Z?
Options a and b are true, while c is false.