Question

Find the z-score for the sample mean for each of the following samples obtained from a population with µ = 60 and σ = 6.

a)M = 55 for a sample of n = 4

b)M = 65 for a sample of n = 9

Answer 1

Solution,

Given that,

mean = = 60

standard deviation = = 6

a) n = 4

=   = 60

= / n = 6 / 4 = 3

M = 55

z = M - /  

z = 55 - 60 / 3

z = -1.67

b) n = 9

=   = 60

= / n = 6 / 9 = 2

M = 65

z = M - /  

z = 65 - 60 / 2

z = 2.50