Question

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability of success on a single trial
n=6, x=3,p= 0.55

Answer 1

Answer:

0.3032

Step-by-step explanation:

3 parameters [n,x,p] are given. We simply need the formula for binomial distribution and put in the values and solve.

The binomial distribution formula:

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

Where nCx is the combination formula.

Now, we put the numbers and solve:

$P(X=x)=nCx*p^{x}*(1-p)^{n-x}\\P(X=3)=6C3*(0.55)^{3}*(1-0.55)^{6-3}\\P(X=3)=\frac{6!}{(6-3)!*3!}(0.55)^3*(0.45)^3\\P(X=3)=20(0.55)^3*(0.45)^3\\P(X=3)=0.3032$