Question

Assume that a procedure yields a binomial distribution with a trial repeated n=18 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k=5 successes given the probability p=0.51 of success on a single trial.

(Report answer accurate to 4 decimal places.)

Answer 1

0.0278 is the probability

Explanation:

Okay, here we want to find the probability of 5 successes

The best way to go about this is by using the Bernoulli trial

So is p = probability of success = 0.51

Then q = probability of failure = 1-0.51 = 0.49

Mathematically, the Bernoulli approximation for k = 5 out of n = 18 is set up as follows;

P(k = 5) = nCk • p^k • q^(n-k)

P(k = 5) = 18C5 * 0.51^5 * 0.49^13

P(k = 5) = 0.027751047366 which is 0.0278 to 4 decimal places