You have recently been employed at the centre for disease control and prevention

Question

You have recently been employed at the centre for disease control and prevention as Assitant Manager. The manager has asked you to assist in preparing a report on assisted reproductive technologies (ART). ART includes all fertility treatments in which both the egg and the sperm are used. According to data gathered from Central of Diseas Control Prevention, 0.7% of the ART cycles result in an ectopic pregnancy, 33.7% in clinical pregnancy and 65.6% results in no pregnancy.

You randomly selected 10ART cycles for special review report. None of the cycles resulted in clinical pregnancy. The manager feels that it is impossible to select 10ART cycles that did not result in a clinical pregnancy.

a) How would you determine if the manager's view is correct?

b) What probability distribution do you think best describes the situation? Why?

c) Write an explanation that answers the question, "is iot possible to select at randomn 10 ART cycles that did not result in clinical pregnancy?" Include in your explanation the appropriate probability distribution and your calculation of the probability of n o clinical pregnancies in 10ART cycles.

Explanation / Answer

a) The Manager's view is not correct as the given probability of 33.7 % is for the population ( superset of sample ) and not for sample itself. Thereby, when we are taking a sample out of population. There's a possibility that any event can occur. In particular to the question, it's very much possible that all of the ART cycles didn't result in a clinical pregnancy.Adding further, we can compute the probability of occurenence of this event and we will get a non zero probability as computed in part c . This proves that it's possible to have all 10 ART cycles that result in a clinical pregnancy.

b) Binomial distribution with the value of parameters N = 10 and p = 33.7 % best describes the situation as it measures the probability of sucesses in 10 trials i.e. no of ART cycles that resulted in clinical pregnancy. Morever, for any ART cycle selected that's only two possibilities whether it resulted in clinical pregnancy or not.

c) It's possible to select at random 10 ART cycles that did not result in clinical pregnancy. Because it's a possible outcome of the event. The event being selection of 10 ART cycles. For every selected ART cycle , there are two possibilities whether it resulted in clinical pregnancy or not. Thereby, one of the possibilities is that all 10 ART cycles resulted in clinical pregnancy.

Let X be the random variable representing no of ART cycles which resulted in clinical pregnancy out of the selected 10 ART cycles.

p be the probability that the ART cycle resulted in clinical pregnancy. Thereby, p = 33.7%= .337

Pr [ X=0 ] = 10C0 * p0 * (1-p)10 .
   = (1-.337)10
   = (.663)10
   = .016411009

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