In a random birth the probability of a boy is about 51 You a

In a random birth, the probability of a boy is about 51%. You are interestd in the probability that at most half the newborns in a nursery are boys. In particular, you are interested in how this probability changes as the number of newborns increase. Let n be the number of newborns in the nursery.

a). Using a normal approximation with continuity correction, determine the probability that at most n/2 of the newborns in the nersery are boys when: n=100? n=500? n=1000? What conclusion do you reach?

b). Repeat the calculations in part a without correcting for continuity. Is it more important to correct for continuity when n is large or small? Why do you think this is so?

Solution

a)

1)

2)

3)

(B)

2)

3)

We notice that when n is large, continuity correction produces the same answer as the answer we get without using integer continuity