Concept explainers
For a population with
- Find the a-score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.)
- For given mean and standard deviation (SD) find Z score for given X values.
- To find corresponding X value for given Z scores.
Answer to Problem 4P
Solution:
- a) For given
Table (a)
mean | 60 |
sd | 12 |
X(given) | Z=(X-mean)/sd |
75 | 1.25 |
48 | -1 |
84 | 2 |
54 | -0.5 |
78 | 1.5 |
51 | -0.75 |
b) For given
Table (b)
mean | 60 |
sd | 12 |
Z(Given) | X(=Z* sd+mean) |
1 | 72 |
0.25 | 63 |
1.5 | 78 |
-0.5 | 54 |
-1.25 | 45 |
-2.5 | 30 |
Explanation of Solution
Given:
- a) Populations with
b) Populations with
Key Point:
- a) In order to calculate Z scores using the given mean, SD (standard deviation) and X values we have to use the formula for Z scores which is
b) In order to calculate X scores using the given mean, SD and Z values we have to use the formula:
Calculation:
a)
Let's calculate Z for
Presented in Table (a)
b)
Let's calculate X for
Conclusion:
Z score for given X values are calculated and given in Solution (Table a) and X values for given Z scores are calculated and presented in Solution (Table b).
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Chapter 5 Solutions
STATISTICS F/THE BEHAV.SCI.-W/ MINDTAP
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning