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 p of success on a single trial.n=22, x=18, p=0.85, q=.15
To find the probability of x successes given the probability p of success on a single trial, and using the binomial probability formula, we'll need to substitute the given values into the formula.
The binomial probability formula is:
P(x) = nCx * p^x * q^(n-x)
Where:
P(x) is the probability of x successes
nCx is the number of combinations of n items taken x at a time
p is the probability of success on a single trial
q is the probability of failure on a single trial (1 - p)
n is the number of trials
x is the number of successes
Now let's substitute the values into the formula:
P(x=18) = 22C18 * 0.85^18 * 0.15^(22-18)
To calculate the combination part (nCx), we use the formula:
nCx = n! / (x! * (n-x)!)
n! represents the factorial of n, and x! represents the factorial of x.
So for our calculation:
22C18 = 22! / (18! * (22-18)!)
Now, let's substitute all the values into the formula and calculate the probability:
P(x=18) = (22! / (18! * 4!)) * 0.85^18 * 0.15^4
To simplify the calculation, you can use a calculator or a software program that has the factorial function and can handle calculations involving large numbers.
After substituting the values and calculating, you'll find the probability of x=18 successes in the given scenario.