Question

Find the z-score corresponding to X =40 and theX value corresponding to z = 0.25 foreach of the following populations.a. μ = 50 and o = 20b. μ = 50 and o = 4c. μ = 30 and o= 8d. μ = 30 and o = 4

Answer 1

a) We have a distribution with mean 50 and standard deviation of 20.

We can find the z-score for X = 40 as:

$z=\frac{X-\mu}{\sigma}=\frac{40-50}{20}=\frac{-10}{20}=-0.5$

We can find the X given that z = 0.25 as:

$X=\mu+z\sigma=50+0.25\cdot20=50+5=55$

b) For a distribution with mean 50 and standard deviation of 4, the z-score for X = 40 is:

$z=\frac{X-\mu}{\sigma}=\frac{40-50}{4}=\frac{-10}{4}=-2.5$

We can calculate X for z = 0.25 as:

$X=\mu+z\sigma=50+0.25\cdot4=50+1=51$

c) For a distribution with mean 30 and standard deviation of 8, the z-score for X = 40 is:

$z=\frac{X-\mu}{\sigma}=\frac{40-30}{8}=\frac{10}{8}=1.25$

We can calculate X for z = 0.25 as:

$X=\mu+z\sigma=30+0.25\cdot8=30+2=32$

d) For a distribution with mean 30 and standard deviation of 4, the z-score for X = 40 is:

$z=\frac{X-\mu}{\sigma}=\frac{40-30}{4}=\frac{10}{4}=2.5$

We can calculate X for z = 0.25 as:

$X=\mu+z\sigma=30+0.25\cdot4=30+1=31$

Answer:

a) z = -0.5, X = 55

b) z = -2.5, X = 51

c) z = 1.25, X = 32

d) z = 2.5, X = 31