I been trying to figure this out for so long, i just dont get it. if anyone can explain the answer it'd be very much appreciated.


A box of 100 machine components is delivered to a factory: experience shows that the components fail 2% of the time. A random sample of
5 components is tested to see if they function correctly.


Which of the following random variables can represent the events "a component functions correctly" and "a component does not function correctly"?

(a) Z~ N (0, 1).
(b) X ~ Bernoulli with Pr (X = 1) = 0.02.
(c) U ~ U (0, 5).
(d) Y ~ Bin (0.02, 5).
(e) V ~ Poisson (0,02).



Which of the following random variables can represent the number of defective components found in the random sample of 5 components?

(a) Z~ N (0, 1).
(b) X ~ Bernoulli with Pr (X = 1) = 0.02.
(c) U ~ U (0, 5).
(d) Y ~ Bin (0.02, 5).
(e) V ~ Poisson (0,02).




A random sample of size 25 is drawn from a population represented by the random variable Z ~N (0, 1): What is the probability distribution of the sample mean Z obtained from this random sample?

thanks!!