Question

Assume that a procedure yields a binomial distribution with a trial repeated n = 5 times. Use the applet or excel to find the cumulative probability distribution given the probability p = 0.53 of success on a single trial. Notice that we are no longer looking for P(X = k), but instead PIX<k). This is a Cumulative! (Report answers accurate to 4 decimal places.) PIX <k) OM 1993 here to search

Answer 1

Binomial probability is given by
P(X=x) = C(n,x)*px*(1-p)(n-x)
Sample size , n =    5
Probability of an event of interest, p =   0.53

P ( X = 0) = C (5,0) * 0.53^0 * ( 1 - 0.53)^5=		0.0229
P ( X = 1) = C (5,1) * 0.53^1 * ( 1 - 0.53)^4=		0.1293
P ( X = 2) = C (5,2) * 0.53^2 * ( 1 - 0.53)^3=		0.2916
P ( X = 3) = C (5,3) * 0.53^3 * ( 1 - 0.53)^2=		0.3289
P ( X = 4) = C (5,4) * 0.53^4 * ( 1 - 0.53)^1=		0.1854
P ( X = 5) = C (5,5) * 0.53^5 * ( 1 - 0.53)^0=		0.0418

answer is:

X		P(X<=K)
0		0.0229
1		0.1522
2		0.4439
3		0.7728
4		0.9582
5		1.0000