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Z-score, Normal Probability & Percentiles

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1. Consider the following scores comprising a population of size N = 14

X F
14 1
13 2
12 4
11 3
10 2
9 2

A. What is the mean for these N = 14 scores?
B. What is the mode for these N = 14 scores?
C. What is the standard deviation for these N = 14 scores?

2. Using a mean of 7.55 and a standard deviation of 1.86, convert the following values of X into z-scores:
A. X = 10.48, z =
B. X = 3.17, z =
C. X = 8.41, z =
D. X = 5.62, z =

3. Assuming a mean of 7.55 and a standard deviation of 1.86, what is the probability that:
A. p(X > 10.48)
B. p(X < 3.17)
C. p(X < 8.41)
D. p(X > 5.62)

4. Assuming a normal distribution, what values of z corresponds to the following percentiles?
A. 75th
B. 25TH
C. 40TH
D. 60TH
E. 50TH

PLEASE SHOW ALL STEPS REQUIRED TO SOLVE EACH PROBLEM.

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The solution provides step by step method for the calculation of z-score and probability using the Z score. Formula for the calculation is also included.

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1. Consider the following scores comprising a population of size N = 14

X F
14 1
13 2
12 4
11 3
10 2
9 2

Answers

X F X2 X * F X2 * F
14 1 196 14 196
13 2 169 26 338
12 4 144 48 576
11 3 121 33 363
10 2 100 20 200
9 2 81 18 162
Total 14 159 1835

A. What is the mean for these N = ...

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