Binomial distribution

Question

X is a random binomial variable with a mean of 7 and a standard deviation of √2.1. Find

(i) the probability of success, p

(ii) the probability of failure, q

(iii) the number of trials, n

(iv) P(X=4)

Answer 1

Use the formulas for a mean (np) and standard deviation - sqrt(npq)

And don't forget q = 1 - p

So you have a system of equations with 2 unknowns:

7 = n * p

sqrt(2.1) = sqrt ( np(1-p) )

Could you solve it? So, you find n, p

Then q = 1-p

P(x=4) you will find with the calculator, or using binomial formula