If x10 and s3 calculate X for the following z scores a z25 b

If x=10 and s=3, calculate X for the following z scores:

a) z=-2.5

b) z=1

c) z=3.75

Solution

If x=10 and s=3, calculate X for the following z scores:
a) z=-2.5
b) z=1
c) z=3.75

Normal Distribution
Mean ( u ) = 10
Standard Deviation ( sd )=3
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
z=-2.5
=> -2.5 = X- 10 / 3
=> X = -2.5*3 + 10 = 2.5

b)
z=1
=> 1 = X- 10 / 3
=> X = 1*3 + 10 = 13

c)
z=3.75
=> 3.75 = X- 10 / 3
=> X = 3.75*3 + 10 = 21.25