Question

In the exercise, X is a binomial variable with n = 7 and p = 0.2. Compute the given probability. Check your answer using technology. HINT [See Example 2.] (Round your answer to five decimal places.)

P(1 ≤ X ≤ 3)

Answer 1

Solution:

We are given that X is a binomial random variable.

We are given n = 7, p = 0.2

We have to find P(1≤X≤3)

P(1≤X≤3) = P(X=1) + P(X=2) + P(X=3)

P(X=x) = nCx*p^x*q^(n – x)

Where, q = 1 – p = 1 – 0.2 = 0.8

P(X=1) = 7C1*0.2^1*0.8^(7 – 1)

P(X=1) = 7C1*0.2^1*0.8^6

P(X=1) = 7*0.2* 0.262144

P(X=1) = 0.367002

P(X=2) = 7C2*0.2^2*0.8^(7 – 2)

P(X=2) = 7C2*0.2^2*0.8^5

P(X=2) = 21*0.04* 0.32768

P(X=2) = 0.275251

P(X=3) = 7C3*0.2^3*0.8^(7 – 3)

P(X=3) = 7C3*0.2^3*0.8^4

P(X=3) = 35*0.008*0.4096

P(X=3) = 0.114688

P(1≤X≤3) = P(X=1) + P(X=2) + P(X=3)

P(1≤X≤3) = 0.367002 + 0.275251 + 0.114688

P(1≤X≤3) = 0.756941

Required probability = 0.756941

By using excel command

=binomdist(3,7,0.2,1) - binomdist(0,7,0.2,1)

We get required probability as 0.756941

We get same probability as above.