If random variable X follows the Binomial distribution XBino

If random variable X follows the Binomial distribution: X~Binomial(8,0.7), which among the following statements is/are correct?

Solution

Answer : f) P(X<=20) = 1 is Correct

Explanation why other options are rejected :

a. X can have 9 different values from 0 to 8

b. P(X>=3) +P(X<=3) = 1 + P (X=3)

c. P(X<6)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)

d. P(X>6)= P(X=7) + P (X=8)

e. P(2<X<=4)=P(X<=4)-P(X<2)

f. P(X<=20) = P(X=0)+P(X=1)+........+P(X=8) = 1