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As a part of a new healthcare reform, hospitals must report incidence of specific demographic and...

As a part of a new healthcare reform, hospitals must report incidence of specific demographic and health care outcomes to maintain funding. Within this report, it was found that 23.3% the Medicare population in Westmoreland county is Diabetic. As part of a random survey to determine if current preventative measures are helping to target this, a random sample of 50 individuals within the Medicare population we sampled.

Let X be the number of individuals who are Diabetic.

  1. Can X be considered a binomially distributed random variable? Why?
  1. Identify n and p for this problem.
  1. Can variables X be well-approximated by normal random variables?
  1. What is the expected number of diabetic individuals for this problem?
  1. What is the variance for the number of diabetic individuals for this problem?
  1. How many combinations are possible that consists of exactly 20 people that are diabetic?
  1. What is the probability of observing 20 diabetic individuals?

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