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

Answer

• a. Z = 0.20

,

• b. Z = –0.60

,

• c. Z = 3.00

Explanation

Given

• μ = 80

,

• σ = 20

The Z-score formula is given by:

$Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

a.

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

$Z=\frac{82-80}{\frac{20}{\sqrt{4}}}=0.20$

b.

Considering that x = 76 and n= 9:

$Z=\frac{76-80}{\frac{20}{\sqrt{9}}}=-0.60$

c.

Considering that x = 90 and n= 36:

$Z=\frac{90-80}{\frac{20}{\sqrt{36}}}=3$