Consider a binomial experiment with n = 20 and p = .70. A. Compute f(12).
B. Compute f(16).
C. Compute P(x 16).
D. Compute P(x 15).
E. Compute E(x).
F. Compute Var(x).

Complete question:

Consider a binomial experiment with n = 20 and p = .70.

A. Compute f(12).

B. Compute f(16).

C. Compute P(x≥ 16).

D. Compute P(x≤15).

E. Compute E(x).

F. Compute Var(x).

a) 0.1144

b) 0.1304

c) 0.2375

d) 0.7625

e) 14

f) 4.2

Step-by-step explanation:

Given:

n = 20

p = 0.70

q = 1 - p ==>  1 - 0.70 = 0.30

a) Use the formula:

Thus,

b)

c) Compute P(x≥16):

P(x ≥ 16) = P(16) + P(17) + P(18) + P(19) + P(20)

d) P(x ≤ 15):

= 1 - P(x ≥ 16)

= 1 - 0.2375

= 0.7625

e) E(x): use the formula, n * p.

= n*p

= 20 * 0.7

= 14

f) Var(x)

Use the formula: npq

npq = 20 * 0.7 * 0.3

= 4.2

σ