stat stat stat stat

Question

Suppose 400 automobiles are to be inspected for emissions where 50 of them have higher emissions than the allowed limit. A sample of 10 cars is chosen at random and the number of cars that have higher emission values is counted. Thus, it is distributed as Hypergeometric.

a. What is the probability that 6 of them will have a higher emission value?

b. Check whether Binomial approximation can be used to calculate this probability.

c. Find the probability in part (a) by the use of Binomial approximation and compare your results

Answer 1

a. 50 6 350 4

C C

--------------------------------- = 0.0004

400 10

C

b. For large sample size we can use normal approximation to binomial distribution, however, since the sample size is not large and we are not sampling with replacement, the binomial distribution would not apply.

c. Using binomial formula:

C (0.125)^6 (0.875)^4 = 0.0005

10 6