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# Probability calculations based on Z score.

1. For a population with µ=50 and &#963;=10,
A. What is the z-score for X=55, X=60, X=75, X=45, X=30 and X=35?
B. Find the X value that corresponds to each of the following z-scores, z=1.00, z=0.80, z=1.50, z= -0.50, z= -0.30 and z= -1.50.

2. Find the z-score corresponding to a score of X=60 for each of the following distributions.
A. µ=50 and &#963;=10
B. µ=50 and &#963;=5
C. µ=70 and &#963;=20
D. µ=70 and &#963;=5

3. For a sample with a mean of M=85, a score of X=90 corresponds to z=0.50. What is the sample standard deviation?

4. In a population of exam scores, a score of X=88 corresponds to z=+2.00 and a score of X=79 corresponds to z= -1.00. What is the means for the population? What is the standard deviation for the population?

5. A distribution with a means of µ=38 and a standard deviation of &#963;=20 is being transformed into a standardized distribution with µ=50 and &#963;=10. Find the new, standardized score for each of the following values from the original population.

A. X=48
B. X=40
C. X=30
D. X=18

PLEASE SHOW STEP BY STEP HOW YOU SOLVE THESE PROBLEMS.