Assume the cholesterol levels in a certain population have m

Assume the cholesterol levels in a certain population have mean µ= 200 and population standard deviation, sigma = 24. The cholesterol levels for a random sample of n = 9 individuals are measured and the sample mean x is determined. What is the z-score for a sample mean x = 180?

Solution

Normal Distribution
Mean ( u ) =200
Standard Deviation ( sd )=24
Number ( n ) = 9
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 180) = (180-200)/24/ Sqrt ( 9 )
= -20/8= -2.5
= P ( Z <-2.5) From Standard NOrmal Table
= 0.0062                  

Z score is -2.5