Question

Consider a binomial probability distribution with

p=0.4 and n=7

.

What is the probability of the​ following?

​a)	exactly three successes
​b)	less than three successes
​c)	five

or more successes

​a) P( x = 3) =

​(Round to four decimal places as​ needed.)

​b) P (x<3) =

​(Round to four decimal places as​ needed.)

​c) P ( x greater than or equal to 5)=

(Round to four decimal places as​ needed.)

Answer 1

Binomial distribution: P(X) = nCx px qn-x

p = 0.4

q = 1 - 0.4 = 0.6

n = 7

a) P(x = 3) = 7C3 x 0.43 x 0.64

= 0.2903

b) P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2)

= 0.67 + 7C1x0.4x0.66 + 7C2x0.42x0.65

= 0.4199

c) P(x 5) = P(x = 5) + P(x = 6) + P(x = 7)

= 7C5x0.45x0.62 + 7C6x0.46x0.6 + 0.47

= 0.0963