A population of values has a normal distribution with μ=76.6 and σ=43.9

Question

You intend to draw a random sample of size n=142.

Find P75, which is the score separating the bottom 75% scores from the top 25% scores.

Answer 1

Z = (score-mean)/SEm

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.75) and its Z score. Insert data into first equation and solve for score.

Answer 2

That would be for finding the distribution of means. Use the equation:

Z = (score-mean)/SD