Unit 5: Discussion

Directions

Initial Post

Read through the answer postings and responses already posted by classmates. Choose one and only one question that has not been answered previously. Once a question has been answered, it is no longer eligible for you to answer, and will not earn you any points should you post an answer to it.

1. Write the question number in your subject line
2. Copy the question itself in your message body

Discussion Questions

Choose one question below that has not been answered by your peers:

1. What does it take to have a normal distribution?
2. How does a normal and standard normal distribution differ? Graphs are encouraged with your written explanation.
3. Explain the difference in shapes between a distribution with a mean of 1 and a standard deviation of 2, versus one with a mean of 2 and standard deviation of 1. What would happen if you converted both of them to the standard normal distribution?
4. State the Empirical Rule. How does it differ from Chebyshevs Theorem, and how is it the same?
5. For a standard normal distribution, what percentage of the total area is contained within -1 to +2 standard deviations of the mean? How did you determine this?
6. What is the difference between a data value and a z-score? Explain the process for finding a z-score, as well as its meaning.
7. If I know that
8. and
9. for a data set, and that
10. is a data point, what is the equivalent z-score?
11. I am teaching two classes of statistics this semester. Class A had a mean of 67 with a standard deviation of 7 for Exam 1. Meanwhile, Class 1 had a mean of 75 and a standard deviation of 10 for Exam 1. There was a student in each class that earned a 70. How can I compare these two scores to each other. What assumptions must be made?
12. When I was hired by Park, internet research told me that the average salary was $62,000 with a standard deviation of $8,000. If I negotiated an annual salary of $54,000, how did I do? What salary would you have attempted to negotiate for and why?
13. Part of this section is a history lesson. The z-score table (posted in the Module under Materials) used the be the only reliable/ quick way to determine areas under the curve. Record a short video of how you can use this table to find
14. .
15. Part of this section is a history lesson. The z-score table (posted in the Module under Materials) used the be the only reliable/ quick way to determine areas under the curve. Record a short video of how you can use this table to find
16. .
17. Part of this section is a history lesson. The z-score table (posted in the Module under Materials) used the be the only reliable/ quick way to determine z-scores for given areas under a curve. Record a short video of how you can use this table to find the z-score associated with the area 0.60257?
18. Part of this section is a history lesson. The z-score table (posted in the Module under Materials) used the be the only reliable/ quick way to determine z-scores for given areas under a curve. Record a short video of how you can use this table to find the z-score associated with the area 0.01017?
19. In a standard normal distribution, find the z-score that corresponds to the 75th
20. Assume that you are thinking about starting a Mensa chapter in your hometown, which has a population of ~10,000 people. You need to know how many people would qualify for Mensa, which requires an IQ of at least 130. You realize that IQ is normally distributed with a mean of 100 and a standard deviation of 15. Find the approximate number of people in your hometown who are eligible for Mensa. Show all formulas.
21. Assume that you are thinking about starting a Mensa chapter in your hometown, which has a population of ~10,000 people. You need to know how many people would qualify for Mensa, which requires an IQ of at least 130. You realize that IQ is normally distributed with a mean of 100 and a standard deviation of 15. Is it reasonable to continue your quest for a Mensa chapter in your hometown? Explain.
22. Assume that you are thinking about starting a Mensa chapter in your hometown, which has a population of ~10,000 people. You need to know how many people would qualify for Mensa, which requires an IQ of at least 130. You realize that IQ is normally distributed with a mean of 100 and a standard deviation of 15. What would the minimum IQ score be if you wanted to start an Ultra-Mensa club that included only the top 1% of IQ scores?
23. If you take repeated samples from the sample population, would you expect to see the exact same information in each sample? Why or why not?
24. What is the standard deviation of the sample means called? What is the formula for this? Are there any special rules to watch for when trying to apply this?
25. Heights among the population of Park students is normally distributed, where
26. inches and
27. inches. If I take a sample of 15 students and record their average heights, what would you estimate the sample average and sample standard deviation to be? Why?
28. Scholarship amounts among the population of Park students is NOT normally distributed, where
29. and
30. . If I take a sample of 38 students and record their average scholarship, what would you estimate the sample average and sample standard deviation to be? Why?
31. In graduate school there was a math class with only a final exam and no other graded work. I scored 23% on it. The class average was 27%, and the standard deviation was 6%. How did I do with respect to everyone else? Using the Empirical Rule, what grade range would contain 68% of the students from class? Assume the information is normally distributed.
32. On average a person in the United States sleep 7.2 hours per night, with a standard deviation of 1.3 hours. What is the probability that a randomly selected person sleeps less than 6 hours? Explain all work and show all formulas used.
33. On average a person in the United States sleep 7.2 hours per night, with a standard deviation of 1.3 hours. What is the probability that a randomly selected person sleeps more than 9 hours? Explain all work and show all formulas used.
34. On average a person in the United States sleep 7.2 hours per night, with a standard deviation of 1.3 hours. What is the probability that a randomly selected person sleeps between 5 and 8 hours? Explain all work and show all formulas used.

I chose to write about question 32 which is actually number 23, for this discussion.