Answer: mean= 40 and standard deviation= 12
Step-by-step explanation:
in the attachment
Answer:
mean=40
standard deviation=12
Step-by-step explanation:
We want to estimate mean and standard deviation for the population.
We know that z-score=(x-mean)/S.d.
sd*z-score+mean=x
σz+μ=x
We are given that for X=28 the z-score is z=-1 and for X=34 the z-score is z=-0.5 so, we have two equations:
For X=28, z=-1
σ(-1)+μ=28
-σ+μ=28 (A)
For X=34, z=-0.5
σ(-0.5)+μ=34
-0.5σ+μ=34 (B)
Subtracting equation A from equation B
-0.5σ+μ-(-σ+μ)=34 -28
-0.5σ+μ+σ-μ=6
0.5σ=6
σ=6/0.5
σ=12
By putting σ=12 in either equation we get the value of μ. Putting value in equation A
-12+μ=28
μ=28+12
μ=40
The values of mean and standard deviation can be verified by putting these values in z-score formula and compute z-score for x=28 and x=34. If the z-score are same as given then values are correct.
Z-score for X=28
Z=(28-40)/12=-12/12=-1
Z-score for X=34
Z=(34-40)/12=-6/12=-0.5
So, the z-scores computed are same as given in the question.
Thus, the required mean is 40 and standard deviation is 12.
