Project 1

IT 403 -- Project 2BCD

Part B: Probabilities for Normal Distributions

Use SPSS to help you solve these problems. Show a printout of your SPSS datasets containing the calculated variables in your output. Check your answers with the normal and extreme normal tables from the textbook. Copies of these tables are also on the Documents Page.
Use the SPSS function Cdf.Normal(z,0,1) to find the area of the standard normal curve for the interval (-∞, z]. Use Idf.Normal(p,0,1) to find the z for which the area of (-∞, z] is p.
1. LSAT scores are normally distributed with mean 150 and SD 10. What percentage of students taking the LSAT test obtain a score
  1. under 142?
  2. over 191?
  3. between 153 and 174?
2. The lengths of horse pregnancies are normally distributed with mean 336 days and SD 3 days. What percent of the lengths of horse pregnancies are between 335 and 338 days?
3. Determine the following percentiles for LSAT scores (see Problem 1 in this part):
  a. 57% b. 98% c. 39%
4. Determine these percentiles for horse pregnancies:
  a. 89% b. 45%

Part C: Random Number Simulations

For this section you only need to include the two normal plots in your output.

Perform two simulations with random numbers to see how the normal plots behave.
1. To create a dataset consisting of 100 normal random numbers with center 5 and spread 3:
  1. Type in using the data editor, a variable that represents the observation number called Number or ObsNum. Cut and paste from Excel to speed up the data entry process.
  2. Select Transform >> Compute Variable. Enter x in the Target Variable box and and Rv.Normal(5, 3) as the expression to compute. Click Ok
2. Create a normal plot of the normal random numbers in Part C, Problem 1.
3. Create a dataset consisting of 100 uniform random numbers, repeat the steps in 1, except use Rv.Uniform(2, 4) as the expression to compute.
4. Create a normal plot of the normal uniform random numbers in Part C, Problem 3.

Part D: Normal Plots

Use SPSS to create the normal plot for the data you collected and analyzed in Project 2A. Use the terms approximately normal, skewed to the right, skewed to the left, fat tails, and thin tails to describe your normal plot.