Question

Let X be a binomial random variable with n = 100 and p = 0.2. Find approximations to these probabilities. (Round your answers to four decimal places.)

(c)    P(18 < X < 30)

(d)    P(X ≤ 30)

Answer 1

Here' answer to the question. Let me know in case you've doubts. Have a good weekend!

Lets use the binomial distribution pdf function to solve this:

we have been the parameters of binomial distribution here ( given that distribution of X is binomial)

c. P(18<X<30) = P(19<=X<=29) [taking care of the limits]

= P(X<=29) - P(X<=18)

To find out the cumulative probability for binomial distribution lets use the Excel formula = BINOMDIST(x,n,p,TRUE)

Lets use this here.

P(X<=29) = BINOMDIST(29,100,.2,TRUE) = .9888

P(X<=18) = BINOMDIST(18,100,.2,TRUE) = .3621

So, P(X<=29) - P(X<=18) = .9888 - .3621 = .6267

Answer is 0.6267 ( 4 digit rounded off)

d. We have been given P(X<=30), which is = BINOMDIST(30,100,.2,TRUE) = .9940

Answer is 0.9940 ( 4 digit rounded off)