Question

For a population with u= 100 and o= 15, find the z-score corresponding to each of the following Xvalues:(a) X=105, Z=(b) X=90, Z=(c) X=135, Z=(d) X=80, Z=

Answer 1

Given:

u= 100

o= 15

Therefore:

a) X=105

`Z=(X-\mu)/(\sigma)=(105-100)/(15)=(5)/(15)=(1)/(3)`

Answer: Z = 1/3

b) X=90

`Z=(90-100)/(15)=(-10)/(15)=-(2)/(3)`

Answer: Z = -2/3

c) X=135

`Z=(135-100)/(15)=(35)/(15)=(7)/(3)`

Answer: Z = 7/3

d) X=80

`Z=(80-100)/(15)=(-20)/(15)=-(4)/(3)`

Answer: Z = -4/3