Question 1018967
 
Question:
In a population of exam scores, a score of X=48 corresponds to Z= +1.00 and a score of X = 36 corresponds to Z = - 0.50. Find the mean and standard deviation for the population.
 
Solution:
Using Z=(X-μ)/σ,
we substitute into the given data:
1.0=(48-μ)/σ
=>
μ+σ=48........(1)
-0.50=(36-μ)/σ
=>
μ-0.5σ=36 .....(2)
 
(1)-(2)
1.5&sigma;=12 =><b>&sigma;=8</b>.....(3)
  
Substitute (3) in (1)
&mu;+8=48 => <b>&mu;=40</b> ......(4)
 
Check:
(48-40)/8=1
(36-40)/8=-0.5
so both are correct.