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

$Z=\frac{X-\mu}{\sigma}=\frac{105-100}{15}=\frac{5}{15}=\frac{1}{3}$

Answer: Z = 1/3

b) X=90

$Z=\frac{90-100}{15}=\frac{-10}{15}=-\frac{2}{3}$

Answer: Z = -2/3

c) X=135

$Z=\frac{135-100}{15}=\frac{35}{15}=\frac{7}{3}$

Answer: Z = 7/3

d) X=80

$Z=\frac{80-100}{15}=\frac{-20}{15}=-\frac{4}{3}$

Answer: Z = -4/3