Question

in a population distribution a score of x=28 corresponds to z=-1.00 and a score of x=34 what is the mean and standard deviation

Answer 1

`x=28\implies z=\frac{28-\mu}\sigma\implies \mu-\sigma=28`


`x=34\implies z=\frac{34-\mu}\sigma\implies \mu+\sigma z=34`

We need the exact value of
`z` to find a proper solution, but a general one can still be found. Subtracting the first equation from the second gives


`(\mu+\sigma z)-(\mu-\sigma)=34-28\implies (z+1)\sigma=6\implies \sigma=\frac6{z+1}`

Plug this into either equation and you get


`\mu-\frac6{z+1}=28\implies \mu=28+\frac6{z+1}`

(It's guaranteed that
`z\\eq-1` in this case because that already corresponds to
`x=28`.)