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Statistical Analysis of Holiday Gifts Return Probability and Distribution Shapes

Analyzing probabilities of returning/exchanging holiday gifts based on survey data, calculating mean, variance, standard deviation, and distribution shapes. Exploring Binomial & Geometric distributions and Normal Approximation.

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Statistical Analysis of Holiday Gifts Return Probability and Distribution Shapes

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  1. Chapter 8 Final Review

  2. Holiday gifts 1 • On the Saturday after Christmas, it has been estimated that about 14.3% of all mall-goers are there to return or exchange holiday gifts. 25 randomly selected customers are surveyed regarding their purposes at the mall. What is the probability that exactly 4 customers are returning/exchanging holiday gifts? At most 4?At least 4?

  3. Holiday gifts 2 • Considering the same information as the last problem, What is the probability that the interviewer will find the someone who is returning/exchanging holiday gifts on exactly the 4th interviewed customer?

  4. Holiday gifts 3 • Again with the 14.3% returning or exchanging holiday gifts and the 25 randomly selected consumers … What is the mean, variance and standard deviation of the number of customers that are returning/exchanging holiday gifts?

  5. Holiday gifts 4 • Again with the 14.3% returning or exchanging … What is the mean, variance and standard deviation of the number of customers that are typically interviewed before finding the first one who is returning/exchanging holiday gifts?

  6. Holiday gifts 5 • What is the probability that the interviewer will have to interview more than 7 customers in order to finally find someone that is a returner/exchanger? (Two approaches) • … More than 10 customers? • … No more than 6?

  7. Shapes • What is the shape of a Binomial Distribution with: • p = 0.5 • p < 0.5 • p > 0.5 • What is the shape of a Geometric Distribution with: • p = 0.5 • p < 0.5 • p > 0.5

  8. Binomial  normal • 31.4% of all women report an irrational fear of mice. An SRS of 7000 women are questioned about their phobias. What is the probability that there will be at least 2267 in this sample that are afraid of mice? Use a Normal Approximation approach. Why is it justified? Could we do this calculation with a class of 30 girls?

  9. Binomial – Think about it • A fair coin (one for which both the probability of heads or tails are both 0.5) is tossed 30 times. The probability that less than 3/5 of the tosses are heads is:

  10. What does p need to be? • Suppose that we select an SRS of size n = 150 from a large population having proportion p of successes. Let X be the number of successes in the sample. For what smallest value of p would it be safe to assume the sampling distribution of X is approximately normal? What if n = 40? What if n = 4000?

  11. What does n need to be? • Suppose that we select an SRS of size n from a large population having proportion p = .08 of successes. For what smallest value of n would it be safe to assume the sampling distribution of X is approximately normal? What if p = .2? What if p = .9995?

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