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.
- Write the question number in your subject line
- Copy the question itself in your message body
Discussion Questions
Choose one question below that has not been answered by your peers:
- What does it take to have a normal distribution?
- How does a normal and standard normal distribution differ? Graphs are encouraged with your written explanation.
- 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?
- State the Empirical Rule. How does it differ from Chebyshevs Theorem, and how is it the same?
- 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?
- 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.
- If I know that
- and
- for a data set, and that
- is a data point, what is the equivalent z-score?
- 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?
- 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?
- 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
- .
- 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
- .
- 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?
- 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?
- In a standard normal distribution, find the z-score that corresponds to the 75th
- 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.
- 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.
- 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?
- 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?
- 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?
- Heights among the population of Park students is normally distributed, where
- inches and
- 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?
- Scholarship amounts among the population of Park students is NOT normally distributed, where
- and
- . 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?
- 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.
- 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.
- 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.
- 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.
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