With reference to Exercise 75, show that the Poisson distribution would have yielded a better approximation.

Exercise 75

Suppose that we want to use the normal approximation to the binomial distribution to determine b(1; 150, 0.05).

(a) Based on the rule of thumb in Section 6, would we be justified in using the approximation?

(b) Make the approximation and round to four decimals.

(c) If a computer printout shows that b(1; 150, 0.05) = 0.0036 rounded to four decimals, what is the percentage error of the approximation obtained in part (b)?

This serves to illustrate that the rule of thumb is just that and no more; making approximations like this also requires a good deal of professional judgment.