Question

Suppose that 20% of the bindings for a textbook are flawed. Suppose we randomly and independently select 20 of the textbooks. Assume sampling with replacement. 5) Referring to Bindings, find the probability that the number of defective bindings in the sample falls between 2 and 5, inclusive.

a) 0.5981 b) 0.4258 c) 0.8042 d) 0.8803 e) 0.7350 6)

Referring to Bindings, find the variance of the number of defective bindings in the sample.

a) 3.0 b) 3.2 c) 4.0 d) 4.3 e) 5.0

Answer 1

This is a binomial distribution

p = 0.2

n = 20

P(X = x) = 20Cx * 0.2^x * (1 - 0.2)^20-x

5) P(2 < X < 5) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

                         = 20C2 * 0.2² * 0.8¹⁸ + 20C3 * 0.2³ * 0.8¹⁷ + 20C4 * 0.2⁴ * 0.8¹⁶ + 20C5 * 0.2⁵ * 0.8¹⁵

                         = 0.7350

Option-e) 0.7250

6) Variance = n * p * (1 - p) = 20 * 0.2 * 0.8 = 3.2

Option-B) 3.2