Binominal questions n 10 p 3 Find Pr 6 Pat most 2 success

Binominal questions: n = 10, p = .3, Find P(r = 6). P(at most 2 successes) P(at least 6 successes) What is the mean of the binomial distribution above? What is the standard deviation? the variance?

Solution

Given that r is binomial with p = 0.3 and n =10

Binomial formula for r successes = 10Cr (0.3)^r(0.7)^10-r

a) P(r=6) = 0.0368

b) P(r<=2) = 0.3828

c) P(r>=6) = 0.0473

Mean of the binomial distribution = np = 3

Variance = npq = 2.1

Std dev = 1.449