SOLUTION: The scores in a Statistics test follow a normal distribution with an average score of 82 and standard deviation of 5. If all students who got 88 to 94 received a "very good", and i

Algebra ->  Statistics  -> Density-curves-and-normal-distributions -> SOLUTION: The scores in a Statistics test follow a normal distribution with an average score of 82 and standard deviation of 5. If all students who got 88 to 94 received a "very good", and i      Log On


   

Question 1192018: The scores in a Statistics test follow a normal distribution with an average score of 82 and standard deviation of 5. If all students who got 88 to 94 received a "very good", and it was announced that only 8 received a very good, how many students took the test?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean is 82.
standard deviation is 5.
all students who got 88 to 94 received very good.
only 8 received very good.
x-score formula is z = (x-m)/sd
z is the z-score
x is the raw score
m is the mean
sd is the standard deviation
low z-score = (88 - 82) / 5 = 1.2
high z-score = (94 - 82) / 5 = 2.4
area between these z-scores is equal to .10687.
take 8 and divide it by that to get 74.85.
that should be your answer.
round to 75 if you need integers.
with population of 75, .10687 * that = = 8.01 which you can round to 8.
you will not get an integer answer so some rounding will be required.