Question

When will we use Binominal Distribution or Poisson Distribution? And explain why we use them in the questions follows:

1. Suppose 1.5 percent of the antennae on new Samsung cell phones are defective. For a random sample of 200 antennas, find the probability that:
None of the antennae is defective.

2.A renowned psychologist is studying the daytime television viewing habits of college students. She believes 45 percent of college students watch soap operas during the afternoon. To further investigate, she selects a sample of 10. What is the probability of finding exactly four watch soap operas?

Answer 1

Let x denote no. of defective antennas Here x sim Bm(200, 0.015) But since n is large & p is very small Such that n/p = 200 times 0.015 = 3 is constant therefore poision approximation is suitable Rightarrow x sim pos(3) p(X = x) = e^- lambda lambda^x/x!: here lambda = 3 psob(None of the antenna is deflective) =p(x = 0) = e^- 3 3^0/0! = e^- 3 = 0.04979 2. Let x denote no. of samples of college students watching soap operas during afternoon. Here x sim Bm(10, 0.45) Here n = 10 as to independent samples are atken & psob of success , p = 0.45 Here, we use Binomial distribution as sample size(n) is small & psob is also not very small p(x = 4) = (10 4) 0.45^4 0.55^6 = 210 times 0.45^4 times 0.55^6 = 0.23837