Question

Marcus reads in a magazine article that 62% of teenagers prefer Batman over Iron Man. He decides to test this so he takes a simple random sample of 50 people at Wal-Mart on a Sunday afternoon. What is the probability that he finds exactly 40 Batman fans? Round to the nearest thousandth.

Answer 1

The probability is 0.003

Explanation:

If 62% prefers Batman, the percentage that prefers Iron man will be (100-62)% = 38%

So the probability of finding a teenager that likes batman will be 62/100 = 0.62

The probability of finding a teenager that prefers iron man will be 38/100 = 0.38

Now, we want to find the probability that out of 50 people at Walmart on a Sunday, exactly 40 prefers Batman

We can use the Bernoulli approximation of the binomial theorem ;

let probability of liking Batman be q and that of iron man be q

Thus the approximation will be;

P(X = 40) = 50 C 40 (0.62)^40 (0.38)^10

= 0.003200147531

To the nearest thousandth, this is 0.003