Probability and Statistics Apply Probability Distribution Requirements

Instructions

This Discussion Board requires you to answer four questions. For each question, do not simply provide an answer; make sure you explain how you arrived at that answer. Please see the corresponding grading rubric to see how each question is assessed. This is an opportunity for you to show your knowledge and understanding of the weekly concepts. You are strongly encouraged to respond to your classmates’ posts with positive and meaningful feedback and will receive up to one point extra credit per discussion board if you do so. This is meant to be a place where we can learn from one another in an engaging and supportive way!

Questions

• In a survey sponsored by Coca-Cola, subjects aged 15-65 were asked what contributes most to their happiness. The table is based on their responses. Determine whether this is a probability distribution. Give two reasons why you believe it is a probability distribution or give two reasons why you believe it does not satisfy the probability distribution requirements.
  

  Survey Results

  CONTRIBUTES MOST TO HAPPINESS	P(X)
  Family	0.77
  Friends	0.15
  Work/Study	0.08
  Leisure	0.08
  Music	0.06
  Sports	0.04

  1. In a recent U.S. Open tennis tournament, among 20 of the calls challenged by the players, 8 were overturned after a review using an electronic system. Assume that when players challenge calls, they are successful in having them overturned 50% of the time. What is the probability that among 20 challenges, 8 or fewer are overturned? Does this result suggest that the success rate is less than 50%? Why or why not?
• Helene claimed that the expected value when rolling a fair die was 3.5. Steve said that wasn’t possible. He said that the expected value was the most likely value in a single roll of the die, and since it wasn’t possible for a die to turn up with a value of 3.5, the expected value couldn’t possibly be 3.5. Who is right? Use a table to help explain your response.
  1. Define the central limit theorem and its relationship to the sampling distribution of sample means. Define how you can approximate a normal distribution from an original population that is not normally distributed.