Question

I have the answers, but I need to know how to get it. I need help.

In a sample distribution, x=56 corresponds to z= 1.00 and x=47 corresponds to z = -0.50.

find the mean and standard deviation for the sample.

____________
Answer:
mean= 50
standard deviation= 6

Answer 1

I wonder if you still need the solution, but here it is:

\[z=\frac{ (x-mean) }{ SD }\] where SD is the standard deviation.

when x=56 and z=1:
\[1=\frac{ 56-mean }{ SD }\]
\[SD= 56- mean \] --> eq. 1
when x=47, z=-0.5:
\[-0.5=\frac{ 47-mean }{ SD }\]
but we have an equation for SD previously, substitute it
\[-0.5=\frac{ 47-mean}{ 56-mean }\]
Solving for mean, you will get 50.
Substitute 50 to get SD:
\[SD=56-mean=56-50=6\]

Answer 2

Yes I do, I'm studying for an upcoming exam :) Thank you! @macro26