Question

A set of data is normally distributed with a mean of 100 and standard deviation of 15.
· What would be the standard score for a score of 85?
· What percentage of scores is between 100 and 85?
· What would be the percentile rank for a score of 85?

Answer 1

A set of data is normally distributed with a mean of 100 and standard deviation of 15.
What would be the standard score for a score of 85?
z(85) = (85-100)/15 = -15/15 = -1
That means 85 is one standard deviation to the left of the mean.

Answer 2

Now one standard deviation from the mean covers 34% of the population.
normal (85,100,100,15) = 0.3413

Answer 3

And the lat one , the tail to the left of 85 must have 0.5000-0.3413 = 0.1587 of te population.
The percentile score must be 15.87% . got it ?

Answer 4

yes I understand now thanks ashna

Answer 5

no mention :)