The Centers for Disease Control and Prevention (CDC) is requir...

Question

The Centers for Disease Control and Prevention (CDC) is required by law to publish a report on assisted reproductive technology (ART). ART includes all fertility treatments in which both the egg and the sperm are used. These procedures generally involve removing eggs from a patient’s ovaries, combining them with sperm in the laboratory, and returning them to the patient’s body or giving them to another patient.

You are helping to prepare a CDC report on young ART patients and select at random 6 ART cycles of patients under 35 years of age for a special review. None of the cycles resulted in a live birth. Your manager feels it is impossible to select at random 10 ART cycles that do not result in a live birth. Use the pie chart at the right and your knowledge of statistics to determine whether your manager is correct.

Bar graph showing live birth rates for ART cycles by age group, with percentages decreasing from 52% for 34 and under to 3.2% for 43 and older.

a. How would you determine whether your manager is correct, that it is impossible to select at random six ART cycles that do not result in a live birth?

Accepted Answer

Welcome back, everyone. A National Roofing Association studied the outcomes of 100 roofing inspections and classified them as described in the pie chart below. You are reviewing the records and randomly select 6 inspections of recently completed roofing jobs and discover that all 6 failed. A team leader claims it is impossible to randomly select 6 inspections that all fail. Use a pie chart to determine whether the team leader's claim is correct and explain why or why not. So for this problem, we're going to use our pie chart which says passed no repairs, 68% passed with minor repairs, 22% and failed 10%. And we're going to model this situation as a binomial experiment where the number of trials N is 6. Now for the probability of success, we're actually going to consider those inspections that failed and we're given 10% or 0.10 in its decimal form, and the complement of that would be those inspections that passed 22% plus 68%, that's 90% or 0.90%. We want to determine the probability that our random variable X where defining X as the number of inspections that fail is equal to 6. According to the binomial probability formula, we have to take and choose X. So 6, choose 6. Multiply that by the probability of success, 0.10.a to the power of X, so we're raising is the power of 6, and then we're multiplying by Q, which is 0.90, raise to the power of N minus X. So 6 minus 6 is 0. 626 is 1. So we basically get 0.10 raise to the power of 6 multiplied by 1. Which is 0. 10 raises the power of 6, right? And we can express it in terms of its percentage form by multiplying this result by 100. So we get 0.0001%. As we can see, it is actually possible to have all 6 inspections that all fail, but this probability is very low. So we can basically conclude that. According to the question. We want to identify whether the team leader's claim is correct, so we can say no, it is not correct, and our explanation is very simple. The probability Yes Very low But not 0. Whenever we say impossible, we basically imply that an event has zero probability of occurring. And in this context, this is not the case because our probability is 0.0001%. Thank you for watching.

Key Concepts

Random Sampling

Probability

Statistical Inference

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