Probability Distributions And Questions

Full Answer Section

      Using Normal Approximation for Binomial: A normal distribution can be a good approximation for a binomial distribution when these conditions are met:

• Large Sample Size (n):Generally, n should be greater than 30 (some say 50) for both successes (events) and failures.
• Not Too Close to the Edges:The probability of success (p) shouldn't be too close to 0 or 1 (ideally between 0.2 and 0.8).

Even if these conditions aren't perfectly met, the approximation might still be useful, especially for larger n.

3. Importance of Probability in Public Health:

Knowing probabilities is crucial in public health for:

• Disease Outbreaks:Estimating the probability of an outbreak spreading based on factors like transmission rates and population immunity.
  • Example: Calculating the probability of a new flu strain causing a pandemic based on its contagiousness.
• Screening Programs:Determining the probability of a positive test result being a true positive or a false positive.
  • Example: Estimating the probability of a mammogram detecting cancer when it's actually present.
• Vaccination Effectiveness:Assessing the probability of vaccination preventing a specific disease.
  • Example: Calculating the probability of a measles vaccine preventing measles infection after exposure.
• Resource Allocation:Distributing resources like medications or medical equipment based on the probability of needing them in different areas.
  • Example: Prioritizing vaccine distribution to regions with a higher probability of an outbreak.

By calculating probabilities, public health professionals can make informed decisions about resource allocation, prevention strategies, and intervention plans.  

Sample Answer

   

Here's a breakdown of the differences between binomial and normal distributions, when to use a normal approximation, and the importance of probability in public health:

1. Basic Differences:

• Binomial Distribution:
  • Discrete probability distribution.
  • Represents the probability of getting a certain number of successes ("events") in a fixed number of trials, where each trial has only two outcomes (success or failure).
  • Examples: Flipping a coin 10 times and getting 3 heads, rolling a die 20 times and getting 7 as a result 4 times.
• Normal Distribution:
  • Continuous probability distribution.
  • Represents the probability of a variable occurring anywhere along a continuous spectrum.
  • Examples: Heights of people, blood pressure measurements, scores on an exam.