suppose 20 individuals are randomly selected from a large population of voters of which 40% are democrats. what are the probabilities that:

Question

a) exactly 10 of the selected voters are democrats?

b) at least 10 are democrats?

c) at most 10 are democrats?

d) between 8 and 12, inclusive are democrats?

e) how many of the voters selected could we expect to be democrats?

Answer 1

I used Excel, but you can get the same answers on a hand calculator

a) either use the binomial distribution formula C(20,10)(.4^10)(.6^10) = 184756 * 0.0001048576 * 0.0060466176 = 0.11714155053639 or use =BINOM.DIST(10,20,0.4,0) in Excel and get the same answer; 0 means the pdf rather than the CDF.

b) at least 10 is 1 - P(X <= 9) = = 1 - BINOM.DIST(9,20,0.4,1) = 1 - 0.244662796683607 - note the 1 at the end for cumulative - =

0.244662796683607

c) at most 10 - BINOM.DIST(10,20,0.4,1) is 0.872478753852783

d between 8 and 12 will use P(X <= 12) - P(X <= 7) = BINOM.DIST(12,20,0.4,1) - BINOM.DIST(7,20,0.4,1) = 0.563078134964693

e) np = 20 * .4 = 8