# Normal distribution

• Jun 17th 2007, 10:51 AM
graceofayak
Normal distribution
I am drawing a blank on how to solve this problem. Can somebody help?
"A normal distribution consist of 100 scores with a mean of 65 and a standard deviation of 5. How many scores are above 70 and how many are below 55? :confused:
• Jun 17th 2007, 11:03 AM
CaptainBlack
Quote:

Originally Posted by graceofayak
I am drawing a blank on how to solve this problem. Can somebody help?
"A normal distribution consist of 100 scores with a mean of 65 and a standard deviation of 5. How many scores are above 70 and how many are below 55? :confused:

Badly posed question, the scores may have a normal distribution with mean
65 and SD of 5, but the numbers above 70 and below 55 are random
variables, and so not fixed numbers. We can talk of the percentage of scores
above 70 and below 55, but these will not be the number out of a sample of
100 that are above and below these values (well not often anyway).

RonL

(70 is 1 SD above the mean so looking 1 up in a table of the standard normal
distribution we find 84.13% of scores are below 70, and so 15.87% are above
70. Similarly 55 is 2 SD's below the mean so looking -2 up in the table of the
cumulative standard normal distribution we see that 2.28% of scores are less
than 55.)