# Z-score, Normal Probability & Percentiles

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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#### Solution Preview

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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 = ...

#### Solution Summary

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.