(5) In a lot of 100 light bulbs, there are 5 bad bulbs. An inspector inspects 10 bulbs selected at random. Find the probability of finding at least one defective bulb. Hint: First compute the probability of finding no defectives in the sample.
(8) Of 50 buildings in an industrial park, 12 have electrical code violations. If 10 buildings are selected at random for inspection. Find the following:
A. P(X = 3)
B. Variance of X.
(25) A jar contains 25 pieces of candy, of which 11 are yogurt-covered nuts and 14 are yogurt-covered raisins. Let X equal the number of nuts in a random sample of 7 pieces of candy that are selected without replacement. Find:
A. P(X = 3).
B. P(X = 6).
C. P(X ≤ 3).
D. The Mean of X.
E. The Variance of X.
(15) Suppose there are 3 defective items in a lot (collection) of 50 items. A sample of sixe 10 is taken at random and without replacement. Let X denote the number of defective items in the sample.
A. State the p.m.f of X.
B. Find the probability that the sample contains exactly one defective item.
C. Find the probability that the sample contains at most one defective item.
(12) For a Hypergeometric Distribution: Find the mean, variance and standard deviation if N1 = 16, N2 = 64, and n = 16
(9) An urn contains 7 red and 11 white balls. Draw one ball at random from the urn. Let X = 1 if a red ball is drawn, and Let X = 0 if a white ball is drawn.
A. Give the p.m.f. of X.
B. Find the mean of X.
C. Find the variance of X.