Question

Consider a binomial random variable where the number of trials is 12 and the probability of success on each trial is 0.25. Find the mean and standard deviation of this random variable. I have a mean of 4 and a standard deviation of 2.25 is this correct

Answer 1

For this type of problem:

mean = np = (12)(.25) = 3
standard deviation = √npq = √(12)(.25)(.75) = √(2.25) = 1.5

Note: q = 1 - p

Answer 2

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.
nequals=55​, xequals=22​, pequals=0.65