Question

Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Find the probability distribution given the probability p=0.614p=0.614 of success on a single trial. Report answers accurate to 4 decimal places.

k	P(X = k)
0
1	.0682
2
3
4	.2743
5	.0872

2.)

Suppose that 65% of all voters prefer Candidate A.

If 10 people are chosen at random for a poll, what is the probability that exactly 3 of them favor Candidate A?

Answer 1

1) p = 0.614, n = 5

Binomial distribution using excel:

k	Formula	P(X = k)
0	= BINOM.DIST(0, 5, 0.614, FALSE)	0.0086
1	= BINOM.DIST(1, 5, 0.614, FALSE)	0.0682
2	= BINOM.DIST(2, 5, 0.614, FALSE)	0.2168
3	= BINOM.DIST(3, 5, 0.614, FALSE)	0.3449
4	= BINOM.DIST(4, 5, 0.614, FALSE)	0.2743
5	= BINOM.DIST(5, 5, 0.614, FALSE)	0.0873

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2) Probability of voter that prefer candidate A = 0.65

n = 10

Probability that exactly 3 of them favor Candidate A, P(X=3) =

Using Binomial distribution in excel:

= BINOM.DIST(3, 10, 0.65, FALSE)

= 0.0212