Question

Let X represent a binomial random variable with n = 180 and p = 0.25. Find the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

a. P(X ≤ 45)

b. P(X = 35)

c. P(X > 55)

d P(X ≥ 50)

Answer 1

X represent a binomial random variable with n = 180 and p = 0.25

The probability mass function of X is given as -

We can use Normal Aprroximation to Binomial distribution. But here we will use direct Binomial distribution approach.

a.

P(X ≤ 45) = 0.5399

b.

P(X=35) = 0.0157

c.

P(X>55)=0.0376

d.

P(X ≥ 50)=0.2176