In a random birth, the probability of a boy is about 51%. You are interestd in t

Q: In a random birth, the probability of a boy is about 51%. You are interestd in t

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 n = 100 p = 0.51 For this case, applying normal approximation to binomial, we get: mean = n*p= 51 variance = n*p*(1-p) = 24.99 std dev = 4.999

ID: 3416538 • Letter: I

Question

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?

Explanation / Answer

(B)

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

n = 100
p = 0.51
For this case, applying normal approximation to binomial, we get:
mean = n*p= 51
variance = n*p*(1-p) = 24.99
std dev = 4.999

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In a random birth, the probability of a boy is about 51%. You are interestd in t

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