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Sample Standard Deviations

1. For a sample with a mean of M=45, a score of X=59 corresponds to z=2.00. What is the sample standard deviation?

2. In a population of exam scores, a score of X=48 corresponds to z=+1.00 and a score of X=36 corresponds to z=-0.50. Find the mean and standard deviation for the population.

3. For each of the following populations, would a score of X=50 be considered a central score(near the middle of the distribution) or an extreme score (far out in the tail of the distribution)?
a. µ=45 and σ=10
b. µ=45 and σ=2
c. µ=90 and σ=20
d. µ=60 and σ=20

4. For each of the following identify the exam score that should lead to the better grade. In each case explain your answer.
a. A score of X=56, on an exam with µ=50 and σ=4, or a score of X=60 on an exam with µ=50 and σ=20.
b. A score of X=40, on an exam with µ=45 and σ=2, or a score of X=60 on an exam with µ=70 and σ=20.
c. A score of X=62, on an exam with µ=50 and σ=8, or a score of X=23 on an exam with µ=20 and σ=2.

5. A distribution with a mean of µ=56 and a standard deviation of σ=20 is being transformed into a standardized distribution with µ=50 and σ=10. Find the new. Standardized score for each of the following values from the original population.
a. X=46
b. X=76
c. X=40
d. X=80

6. A sample consists of the following n=6 scores: 2,7,4,6,4, and 7.
a. Compute the mean and standard deviation for the sample
b. Find the z-score for each score in the sample
c. Transform the original sample into a new sample with a mean of M=50 and x=10.

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Solution Summary

The solution gives detailed steps on solving 5 statistical problems using normally distributed data. All formula and calculations are shown and explained.

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