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Jan 21 Statistic for the day: The width of train tracks is 4 feet 8.5 inches. Why?

Jan 21 Statistic for the day: The width of train tracks is 4 feet 8.5 inches. Why?. Assignment: Read Chapter 9 Exercises from Chapter 8: 16, 18. These slides were created by Tom Hettmansperger and in some cases modified by David Hunter.

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Jan 21 Statistic for the day: The width of train tracks is 4 feet 8.5 inches. Why?

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  1. Jan 21 Statistic for the day:The width of train tracks is 4 feet 8.5 inches.Why? Assignment: Read Chapter 9 Exercises from Chapter 8: 16, 18 These slides were created by Tom Hettmansperger and in some cases modified by David Hunter

  2. Research Question 1: How high should I build my doorways so that 99% of the people will not have to duck? Secondary Question 2: If I built my doors 75 inches (6 feet 3 inches) high, what percent of the people would have to duck?

  3. Find the value at Question 1 so that 99% of the distribution is below it. The value at Question 2 is 75; find the amount of distribution above it.

  4. Z-Scores: Measurement in Standard Deviations Given the mean (68), the standard deviation (4), and a value (height say 75) compute Z = (75-mean) / SD = (75-68) / 4 = 1.75 This says that 75 is 1.75 standard deviations above the mean.

  5. Answer to Question 2: What percent of people would have to duck if I built my doors 75 inches high? Recall: 75 has a Z-score of 1.75 From the standard normal table in the book: .96 or 96% of the distribution is below 1.75. Hence, .04 or 4% is above 1.75. So 4% of the distribution is above 75 inches.

  6. The value at Question 2 is 75; find the amount of distribution above it. Convert 75 to Z = 1.75 and use Table 8.1 in book.

  7. Question 1: What is the value so that 99% of the distribution is below it? Called the 99th percentile. • Look up the Z-score that corresponds to the 99th • percentile. From the table: Z = 2.33. • Now convert it over to inches: 2.33 = (h – 68)/4 h = 68 + 2.33(4) = 77.3 Since 77 inches is 6 feet 5 inches, 99% of the distribution is shorter than 77 inches and they will not have to duck.

  8. Find the value at Question 1 so that 99% of the distribution is below it. Look up Z-score for 99th percentile and convert it back to inches.

  9. Compare Heights of Females and Males

  10. Shaquille O’Neal is 7 feet 1 inch or 85 inches tall. How many people in the country are taller? • We will assume that heights are normally distributed • with mean 68 inches and standard deviation 4 inches. • O’Neal’s Z-score is Z = (85-68)/4 = 4.25. In other words • O’Neal is 4.25 standard deviations above the mean! • We would generally consider him from a different population. • 3. There is .000011 above 4.25 standard deviations.

  11. There are roughly 250 million people in US. • 48.8% are over the age of 20. • That is 122 million. • Hence, there should be roughly • .000011 times 122 million • or 1342 people taller than Shaquille O’Neal

  12. Who Is the Tallest Person in Class? What is your Z-Score? What is your percentile? How many PSU students are taller?

  13. Suppose someone claims to have tossed a coin 100 times and got 70 heads. Would you believe them? • We need to know what the distribution of the number of heads in 100 tosses looks like for a fair coin. • We need the mean and standard deviation for this distribution.

  14. What is the mean? • What is the standard deviation? • Let’s suppose the smooth version is bell shaped.

  15. So the distribution of the number of heads in 100 tosses of a fair coin is: • Roughly normal, mean about 50, SD about 5 • What is the Z-score of 70? • Ans: 4 • What is the percentile? • Ans: .999968 or 99.9968% • Now do you believe them? • NO • Weighted coin is a BETTER explanation

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