# Calculating Probabilities Using Z-values

7.12

A random sample is obtained from a population with a mean of 50 and a standard deviation of 12.

A. For a sample of n = 4 scores, would a sample mean of M = 55 be considered an extreme value or is it a fairly typical sample mean?

B. For a sample mean of n = 36, would a sample mean of M = 55 be considered an extreme value or is it a fairly typical sample mean?

7.16

A population of scores forms a normal distribution with of 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 with a mean less than M = 34.

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#### Solution Summary

This problem demonstrates the use of z-scores in elementary statistics.