Question

The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 15%. If 16 calculators are selected at random, what is the probability that more than 5 of the calculators will be defective?

Answer 1

X : Number of calculators will be defective

n : Number of calculators selected at random = 16

p: Probability of a defective calculator = 15% =0.15

q=1-p=1-0.15 = 0.85

X follows a Binomial distribution with n=16 and p=0.15 with Probability mass function :

Probability that there are 'r' of the calculators are defective = P(X=r)

Probability that more than 5 of the calculators will be defective = P(X>5) = 1 - P(X5)

P(X5) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)

P(X5) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5) = 0.0743+0.2097+0.2775+0.2285+0.1311+0.0555=0.9766

P(X>5) = 1 - P(X5) = 1 - 0.9766 = 0.0234

Probability that more than 5 of the calculators will be defective = 0.0234