In: Statistics and Probability
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
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