Answer to Question #214912 in Statistics and Probability for nunez

Question

Ten percent of Americans are allergic to ragweed. Suppose a random sample of 200 people is selected.

4. Evaluate np and n(1 – p). Is it appropriate to use the normal distribution to approximate the binomial distribution? (Round to 2 decimal places)

            np =                             n(1 – p) =                         Enter Y or N

Answer 1

$n=200 \\ p= 10 \; \% = 0.10 \\ np = 200 \times 0.10 = 20.00 \\ n(1 -p) = 200(1-0.10) = 180.00$

It is appropriate to use the normal distribution to approximate the binomial distribution because, here X~Bin(n,p) and n=200 is large then X is approximately N(n,p,q).

Answer: 20.00; 180.00; Y.