The birth control shot is one of the most effective methods of birth control ava

Question

The birth control shot is one of the most effective methods of birth control available, and it works best when you get the shot regularly, every 12 weeks. Under ideal conditions, only 1% of women getting the shot become pregnant within one year. In typical use, however, 3% become pregnant. A study of the effectiveness of the birth control shot interviews a random sample of 650 women who are using the shot as their method of birth control.

What is the approximate probability that at least 28 of these women become pregnant in the next year? (Round your answer to four decimal places.)

Explanation / Answer

X Binomial(n = 650, p = 0.03)
Binomial can be approximated to normal with: u=np= 650*0.03= 19.5
=np = 650*(0.03)(1 — 0.03) = 4.3424 ~ 4.342

P(X > 28)
Normal Distribution
,= 19.5
= 4.342

P(X > 28) = z = X - / = 28-19.5 /4.342 = 1.95

P ( Z>1.95 )
=1P ( Z<1.95 )
=10.9744
=0.0256

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