In a sample distribution, X=56 corresponds to z=1.00 and X=47 corresponds to z=-.50. Find the mean and standard deviation for the sample.

Z = (X-μ) / σ

Since it's the same distribution then they have the same mean μ & the same standard deviation σ

1st Z==> 1 = (56-μ) / σ = = > σ = (56-μ) / 1 = = >σ = (56-μ)

2nd Z = = >-0.5 = (47-μ) / σ==>σ = (47-μ) / (-0.5) = = > σ=-2 (47-μ)

Hence I can write (56-μ) = - 2 (47-μ) = = > μ = 50

Replace μ = 50 in any of the above & you will find σ=6