Normal Distribution of Test Scores: Percentages for Various Ranges

[apoechma]

Scores on a particular test are normally distributed in the population, with a mean of 100 and a standard deviation of 15. What percentage of the population have scores ...

a) Between 100 and 125

b) Between 82 and 106

c) Between 110 and 132

d) Above 132

e) Equal to 132
HELP ME UNDERSTAND THIS PLEASE!

 

[flatmaster]

http://en.wikipedia.org/wiki/Normal_distribution

 

[flatmaster]

THe normal distribution is also know as the Gaussian distribution or a "bell curve" It is described by the equation on the wikipedia page. For your problem
mu = location of the peak probability = 100
sigma^2 = variance = standard variation = 15

You may notice the part of the equation outside the exponential. This is called a normalizing factor. This factor adusts the height of the function depending on the value of sigma so the TOTAL area under the curve is 1. THis means if you the take the test, the probaility that you have any score is 1.

The probability of getting some score between two values is simply the integral of the curve between these two scores. However, it's usless trying to actually do the integral. You need to look up the gaussian integrals in a table.