Question to test your Discrete Random Variables knowledge

Question

A national health agency maintains records on various fertility treatments. One common treatment is intrauterine insemination (IUI), which is less invasive than IVF. The agency publishes a report showing the outcomes of IUI cycles based on patient age groups. This is the data for patients under the age of $30$ :
Successful pregnancy: $25 percent sign$
No pregnancy: $75 percent sign$
You are analyzing the success rate of IUI procedures for a research study. You randomly select $8$ IUI cycles from the under- $30$ age group for a detailed review. None of the selected cycles resulted in a successful pregnancy.
i. Your supervisor argues that it is extremely unlikely to select $8$ cycles with $0$ successful pregnancies randomly. Determine whether your supervisor's concern is valid.
ii. What type of probability distribution would best model the number of successful pregnancies in such samples? Do you think the distribution of successful outcomes is discrete or continuous? Explain your answer.

Accepted Answer

i. No, because 0.10010.1001 is not low enough to be considered unusualii. Distribution: BinomialType: DiscreteReason: Fixed number of independent trials, constant probability of success, and countable outcomes

Answer

i. Yes, because 0.0000150.000015 is extremely low and considered unusual.ii. Distribution: BinomialType: DiscreteReason: Fixed number of independent trials, constant probability of success, and countable outcomes.

Answer

i. No, because 0.10010.1001 is not low enough to be considered unusual.ii. Distribution: PoissonType: DiscreteReason: The scenario measures the occurrence of independent events over a specific sample space.

Answer

i. No, because 0.10010.1001 is not low enough to be considered unusual.ii. Distribution: BinomialType: ContinuousReason: The calculated probability values exist on a continuous spectrum between 00 and 11.

Discrete Random Variables: Videos & Practice Problems