Pharmaceutical companies advertise for the birth control pill an efficacy of 99.

Question

Pharmaceutical companies advertise for the birth control pill an efficacy of 99.5% in preventing pregnancy. However, under typical use, the real efficacy is only about 98%. That is, 2% of women taking the pill for a year will experience an unplanned pregnancy that year. A gynecologist looks back at a random sample of 100 medical records from patients who had been prescribed the pill one year before. What is the probability that the proportion of the women in the sample that experienced an unplanned pregnancy is more than 0.04? Round all interim and final calculations to four decimal places.

Explanation / Answer

Result:

Pharmaceutical companies advertise for the birth control pill an efficacy of 99.5% in preventing pregnancy. However, under typical use, the real efficacy is only about 98%. That is, 2% of women taking the pill for a year will experience an unplanned pregnancy that year. A gynecologist looks back at a random sample of 100 medical records from patients who had been prescribed the pill one year before. What is the probability that the proportion of the women in the sample that experienced an unplanned pregnancy is more than 0.04? Round all interim and final calculations to four decimal places.

n=100, p=0.02

normal approximation to Binomial used.

standard error = sqrt(p*(1-p)/n) = sqrt(0.02*0.98/100) =0.014

z value for 0.04, z =(0.04-0.02)/0.014 =1.43

P( p> 0.04) = P( z >1.43)

=0.0764

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