stat question below in description

Question

A sample size of 50 is selected from a normal distribution having a mean of 95 and a standard deviation equal to 15. What is the probability of selecting a sample having a mean exceeding 100?

Answer 1

You will need the formula for z-score.

 

z = (X - μ) / (σ/√n) = (100 - 95) / (15/√50) = 5/2.12 = 2.36

 

After z-score is found, then you will use the complement rule to figure out the probability of selecting a sample having a mean greater than 100.  Use the z-score table as reference to find the probability.

 

P(Z > 2.36) = 1 - P(Z < 2.36) = 1 - 0.4909 = 0.5091

 

The probability of selecting a sample having a mean exceeding 100 is 0.5091.