Question

We have a normally distributed population of scores with μ = 25 and σ = 5. We have drawn a large number of random samples with a particular sample size of n = 10 from this population. We want to know what the probability that a sample mean will be equal to or greater than 23. First, what is the z-score for our sample mean of interest, 23? Using this z-score , use statistics table to answer the question "What is the probability that a sample mean will be equal to or greater than 23?"

Answer 1

Solution:- Given that μ = 25 and σ = 5., n = 10

P(X >= 23) = P(X > 23.5)

=> P(X > 23.5) = P((X-μ)/(σ/sqrt(n)) > (23-25)/(5/sqrt(10))

= P(Z > -1.2649)

= 0.8962