in a population distribution a score of X 28 corresponds to

in a population distribution, a score of X = 28 corresponds to z= -1.00 and a score of x = 34 corresponds to z = -0.50. find the mean and standard deviation for the population.

Solution

Normal Distribution
Mean ( u ) = Unknown
Standard Deviation ( sd )= Unknown
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

When X = 28, z= -1.00
-1.00 = 28 - U / sd
-s.d = 28 - U
U - s.d = 28 Eqn(1)

When X = 28, z= -1.00
-0.50 = 34 - U / sd
-(0.50)s.d = 34 - U
U - (0.50)s.d = 34 Eqn(2)

Solving Eqn(1)- 2* Eqn(2)

U - s.d = 28
-2U + s.d = - 68
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- U = -40 => U = 40 , Substitute U = 40 in Eqn(1) => 40 - s.d = 28 => s.d = 12