Question

Assume that a procedure yields a binomial distribution with a trial repeated n=9n=9 times. Use either the binomial probability formula (or technology) to find the probability of k=4k=4 successes given the probability p=0.59p=0.59 of success on a single trial.

Answer 1

SOLUTION:

From given data,

Assume that a procedure yields a binomial distribution with a trial repeated n=9 times. Use either the binomial probability formula (or technology) to find the probability of k=4 successes given the probability p=0.59 of success on a single trial.

Where,

n=9

k=4

p=0.59

We know that ,

x bin (n,p) then,

P(X=k) = ⁿCk * p^k * (1-p)^(n-k) Where, ⁿC_k = n! / (k! * (n-k)!)

By substituting the all values,

P(X=4) = ⁹C₄ * (0.59)⁴ * (1-0.59)^(9-4)

P(X=4) = 126 * 0.12117361 * 0.0115856201

P(X=4) = 0.1768