Question

Find the z-score for the sample mean for each of the following samples obtained from a populationwith u= 80 and o= 20.a. M = 82 for a sample of n= 4, Z=b. M = 76 for a sample of n= 9, Z=c. M = 90 for a sample of n= 36, Z=

Answer 1

• a. Z = 0.20

,

• b. Z = –0.60

,

• c. Z = 3.00

Step-by-step explanation

Given

• μ = 80

,

• σ = 20

The Z-score formula is given by:

`Z=(x-\mu)/((\sigma)/(√(n)))`

a.

Considering a mean of x = 82 and a sample of n = 4, then:

`Z=(82-80)/((20)/(√(4)))=0.20`

b.

Considering that x = 76 and n= 9:

`Z=(76-80)/((20)/(√(9)))=-0.60`

c.

Considering that x = 90 and n= 36:

`Z=(90-80)/((20)/(√(36)))=3`