Mathematics for Business Decisions II

General Normal Distributions

For each problem, write out the mathematical expression for what you are computing first using probability notation and then in terms of the specific probability density function for the situation being considered. Then find a numerical approximation rounded to four decimal places using Integrating.xls.

  1. Recall from class the IQ test example. That is, an IQ test for 10-year-olds has a normal distribution with mean 100 and standard deviation 16 (as is typical of cognitive tests).
  2. Find the percentage of 10-year-olds who score within one standard deviation of the mean.
  3. Find the percentage of 10-year-olds who score within two standard deviations of the mean.
  4. Find the percentage of 10-year-olds who score within three standard deviations of the mean.
  5. Find the percentage of 10-year-olds who score more than three standard deviations above the mean.
  6. Experiment in Integrating.xls to find the IQ score corresponding to the 90th percentile (that is, the score that 90% of the population of 10-year-olds will score on or below.)
  7. Experiment in Integrating.xls to find the IQ score corresponding to the 75th percentile (that is, the score that 75% of the population of 10-year-olds will score on or below.)
  1. According to the College Board ( the SAT-I Mathematics Test has a normal distribution with mean 514 and standard deviation 113.
  2. Find the percentage of SAT-I Math test-takers who score within one standard deviation of the mean.
  3. Find the percentage of SAT-I Math test-takers who score within two standard deviations of the mean.
  4. Find the percentage of SAT-I Math test-takers who score within three standard deviations of the mean.
  5. Find the percentage of SAT-I Math test-takers who score more than three standard deviations above the mean.
  6. Experiment in Integrating.xls to find the SAT-I Math score corresponding to the 90th percentile (that is, the score that 90% of the population of SAT-I Math test-takers will score on or below.)
  7. Experiment in Integrating.xls to find the SAT-I Math score corresponding to the 75th percentile (that is, the score that 75% of the population of SAT-I Math test-takers will score on or below.)
  1. Do exercises 15-18 and 21 in Normal Distribution: General Normal. For 21 you will first need to go over Example 5 in the text.