Sketch a normal curve for this distribution, with three standard deviations from the mean marked out.
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- Exercise C1: SAT scores from DoW #5: In DoW #5, we are given thatthe SAT (Scholastic Aptitude Test) scores are normally distributed with μ=896 and σ=174.
(a) Sketch a normal curve for this distribution, with three standard deviations from the mean marked out.
(b) What range of scores is “typical” for this test (with “typical” meaning 95% students score in this range)?
(c) What is the probability that a student would score above 1418?
(d) What is the approximate probability that a student would score between 1200 and 1400? Explain how you found this answer.
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Exercise C2: ACT scores from DoW #5: In DoW #5, we are given that ACT (American College Test) scores are normally distributed with μ=20.6 and σ=5.2.
(a) Sketch a normal curve for this distribution, with three standard deviations from the mean marked out.
(b) What range of scores is “typical” for this test? (with “typical” meaning 95% of students score in this range)
(c) What is the probability that a student would score below 15.4?
(d) What is the approximate probability that a student would score between 15 and 30? Explain how you found this answer.
Exercise C3: Bobby’s Test Scores: In DoW #5, we learn that Bobby scored 1080 on the SAT and 30 on the ACT. Consider your work in Exercises C1 and C2. Which score do you think Bobby should send to his colleges? Why?
- Exercise E2: Complete the Central Limit Theoremdocument.BELOW
PART I
This is the dot plot for a random sample of 50 SAT scores. Describe the shape of the data. Does it appear it will have a relatively large or small standard deviation?
PART II
This graph is from “Collection Means from Random Samples of 50 SAT Scores”. It contains the means collected from 355 samples of 50 SAT Scores.
The Graph at the right shows the distribution of these 300+ sample means.
1. Describe this distribution of sample mean SAT scores. Would you consider it to be nearly normal? How does it compare to the distribution of SAT Scores in Part I?
2. What is the mean of SampleMean50? What is the standard deviation? How do these values compare to the known parameters for the SAT (the mean is 896, the standard deviation is 174).
3. In DoW #5, the sample of 50 SAT Prep students has a mean SAT score of 1000. Where would a mean score of 1000 fall on this graph? How likely is it, based on this data, that a group of 50 studentswould have a mean score of 1000?
- IN this exercise, you will run a virtual experiment to collect random samples of 50 SAT scores and calculate their means. This will produce a distribution of sample means that you can compare to the sample mean for SAT Prep.
Exercise E3: In Exercise E2, you answered the question, “do you think there sufficient evidence to conclude that SAT Prep improves SAT scores, as they claim?”
