Find the probability and standard deviation?

Suppose the discrete random variable X denotes the number of successes that is observed in n = 6 independent


binary trials with the probability of success p = 0.45 .





A)The probability of observing five or more successes is:


B)The standard deviation of the random variable X is:|||A) P(X 鈮?5) = P(X=5) + P(X=6) = choose(6,5) 0.45^5 0.55^1 + choose(6,6) 0.45^6 0.55^0





= 0.06089428 + 0.008303766 ~= 0.0692





B) Variance = 6 x 0.45 x 0.55 = 1.485. s.d = 鈭?.485 = 1.2186|||Let X be the discrete random variable the number of successes that is observed.





p = 0.45





q = 1 - 0.45 = 0.55





n = 6





A)





P(X 鈮?5) = P(X = 5) + P(X = 6) = 0.06089428125 + 0.008303765625 = 0.06919804688





P(X = 5) =





(6)


(5)*(0.45^5)*(0.55)^1 = 0.06089428125





(6)


(6)*(0.45^6)*(0.55)^0= = 0.008303765625





B)





SD(X) = sqrt(n*p*q) = sqrt(6*0.45*0.55) = 1.218605761