Question

Consider a binomial probability distribution with p=.35 and n=7. what is the probability of the following?

a. exactly three successes P(x=3)

b. less than three successes P(x<3)

c. five or more successes P(x>=5)

Answer 1

Let X be a binomial random variable with p = 0.35 and n=7

X ~ Binomial ( n = 7, p = 0.35)

Using Excel we find following probabilities,

a) P(X = 3) = BINOMDIST(3, 7, 0.35, 0) = 0.26787094

=> P(X = 3) = 0.2679 (rounded to 4 decimal places)

b)

P(X < 3)

= P(X <= 2)

= BINOMDIST(2, 7, 0.35, 1)

= 0.53228332

=> P(X < 3) = 0.5323 (rounded to 4 decimal places)

c)

P(X >= 5)

= 1 - P(X < 5)

= 1 - P(X <= 4)

= 1 - BINOMDIST(4, 7, 0.35, 1)

= 0.05560754

=> P(X >= 5) = 0.0556 (rounded to 4 decimal places)