Question

Assume that a procedure yields a binomial distribution with a trial repeated n = 14 n = 14 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k = 14 k = 14 successes given the probability p = p = 23/30 of success on a single trial. (Report answer accurate to 4 decimal places.) P ( X = k ) =

Answer 1

solution:

Given data

sample size (n) = 14

Probability of success (p) = 23/30

k = 14

Let X be the random variable representing the no.of success

X~B(n,p)

~B(14, 23/30)

P(X=x) = nCx * (p)^x * (1-p)^n-x

Now, P(X=k) = P(X=14)

= 14C14 * (23/30)^14 * (7/30)^0

= 0.0242

   $\therefore$ For k=14 , P(X=k) = 0.0242