Question 1068826
mean = 43.9
standard deviation = s
probability that a score is less than 40 is 1/3.


use the z-score table to find the z-score that has an area to the left of it as 1/3 = approximately .3333


you will find that the z-score is equal to somewhere between -.43 and -.44.


since it's closer to -.43, we'll use that.


formula for z-score is z = (x-m)/s


z is the z-score
x is the raw score
m is the mean
s is the standard deviation


using what we know, the formula becomes:


-.43 = (40-43.9)/s


solve for s to get s = -3.9/-.43 = 9.069767 rounded to 6 decimal places.


to find the probability that a z-score is greater than 80% of the population, look for the area to the left of the z-core of .80.


you will find that the z-core is between .84 and .85.


since it is close to .84, we'll use that.


same z-score formula of z = (x-m)/s becomes:


.84 = (49-43.9)/s.


solve for s to get s = 5.1/.84 = 6.071429 rounded to 6 decimal laces.


since the two standard deviations are different, you can conclude that each scenario used a different population.


if they were the same population, the standard deviation should have been the same.


the z-score table that i used can be found at the following link:


http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf