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