IT 223: Data Analysis and Statistical Software
Winter 2006

Assignment 2

Due Friday January 20 before 11:30pm by DL Web Submission

Overview

For this assignment, you will solve some problems using the normal distribution. For the second part, you will compare your data to the normal distribution and make some predictions using the normal distribution as a model. You will then test your predictions against the actual data.

Part I: Problems

These problems are adapted from the questions on page 88 in the text.

In a recent year for graduating high school seniors, the mean ACT score was 20.8 and the standard deviation was 4.8. In the same year, the mean SAT score was 1026 and the standard deviation was 209. Both sets of test scores roughly follow a normal distribution.

Even though the test scores have different ranges (the ACT ranges from 1 to 36 and the SAT ranges from 400 to 1600), it is possible to compare scores from the different tests by calculating their z-scores. With this in mind, answer the following questions:

  1. Tonya scores 1318 on the SAT. Jermaine scores 27 on the ACT. Assuming that both tests measure the same thing, who has the higher score?
  2. What is the percentile for Tonya's SAT score? That is, what percentage of students scores lower than Tonya?
  3. A student scores 1287 on the SAT. What would be the comparable score on the ACT?
  4. If your goal is to score in the top 10% on the ACT, what ACT score would you need?
  5. What proportion of students scored between 15 and 25 on the ACT?

Part II: Analysis

Choose one of your set of timings from the last assignment. Perform the following analysis:

  1. Briefly summarize how you collected your selected set of timings.
  2. Provide the mean, median and standard deviation.
  3. Provide the frequency bar chart and the normal quantile plot.
  4. In a short paragraph, discuss the extent the distribution approximates a normal curve. Use properties discussed in class.
  5. If this distribution were a normal distribution, how many data points would be within one standard deviation of the average?
  6. How many timings actually are within one standard deviation of the average?
  7. Create a second dataset whose values are the natural log (base e) of the values in the first set. Provide the mean, median and standard deviation.
  8. Provide the frequency bar chart and the normal quantile plot of the second dataset.
  9. In a short paragraph, discuss the extent the distribution approximates a normal curve. Use properties discussed in class.
  10. If this distribution were a normal distribution, how many data points would be within one standard deviation of the average?
  11. How many timings actually are within one standard deviation of the average?

Submission

Submit a report that responds to the numbered instructions using the DLWeb submission. All answers, graphs and writing should be contained in one document.