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=(X-\mu)/(\sigma)=(40-50)/(20)=(-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=(X-\mu)/(\sigma)=(40-50)/(4)=(-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=(X-\mu)/(\sigma)=(40-30)/(8)=(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=(X-\mu)/(\sigma)=(40-30)/(4)=(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