Statistics- z-scores,mean,standard deviation

[n77ler]

Homework Statement

Suppose that 40 and 90 are two measurements of a population data set and that their z-scores are -2 and 3, respectively. Using only this information, is it possible to determine the population's mean and standard deviation? If so, find them. If not, explain why it's not possible.

Homework Equations

The Attempt at a Solution

Well 40 and 90 are two data numbers that we are given. Z-scores are deviations from the median of the data set. So the 90 in the population is 3 deviations to the right of the median. 40 is 2 deviations to the left of the median. So if 40 makes the z-score -2 and 90 makes it 3 can I relate them to come up with the median? I've been juggling the numbers but nothing I do seems to come up with a logical answer.

 

[HallsofIvy]

One "relevant equation" would be
[tex]z= \frac{x-\mu}{\sigma}[/itex]

Now stop "juggling numbers" and write down equations!
As you say "90 is 3 deviations right of the mean"(NOT median!): $90= \mu+ 3\sigma$
"40 is 2 deviations to the left of the mean": $40= \mu- 2\sigma$

Now that looks to me like two linear equations to solve for $\mu$ and $\sigma$.

 

[n77ler]

Actually after I posted I realized I messed up that terminology but had to go pick up family so I didn't have time to edit lol.

OK so, 90=x+3y
x=-3y+90

40=x-2y
40= (-3y+90)-2y
40=-5y+90
y=10

x=-3(10)+90
x=60

So mean= 60 and deviation = 10