Let x be the random variable representing defective phone. Let n be the sample size. Let p be the probability that phone is defective.
Given: n=500, p= 0.02
From given information we know that x is random variable such that p is the probability of success and it is constant for each trial. Sample size n is fixed.
X follows Binomial distribution with parameters n=500 and p=0.02
a). The average number of defective phone
E(x) = n*p = 500 * 0.02 = 10
The average number of defective phones is 10.
b)Probability of getting 5 defective phones.
P(X=5) = [tex] (nCx) p^{x} (1-p)^{n-x} [/tex]
= [tex] (500C5) 0.02^{5} (1-0.02)^{500-5} [/tex]
= 0.037
The probability of getting exactly 5 defective is 0.037.
