# Compute z-scores given populations and sample size

For a population with a mean of 60 and a standard deviation of 24, find the z-score corresponding to each of the following samples.

a. M = 63 for a sample of n = 16 scores

b. M = 63 for a sample of n = 36 scores

c. M = 63 for a sample of n = 64 scores

A population of scores forms a normal distribution with a mean of 40 and a standard deviation of 12.

a. What is the probability of randomly selecting a score less than X = 34?

b. What is the probability of selecting a sample of n = 9 scores with a mean less than M = 34?

c. What is the probability of selecting a sample of n = 36 scores with a mean less than M = 34?

https://brainmass.com/statistics/z-test/z-scores-populations-sample-size-309870

#### Solution Preview

(1) z = (M - mu)/(sigma/sqrt n)

(a) z = (63 - 60)/(24/sqrt 16) = 0.5

(b) z = (63 - 60)/(24/sqrt 36) = ...

#### Solution Summary

Provides steps necessary to determine z-score corresponding to each sample.