sub parts 14-16 14. What well-being score represents the 90th percentile?15. What well-being score represents the 50th percentile?16. What well-being score represents the 66th percentile? For your doctoral dissertation, you decide to study the social well-being of 100,000 people. You ask them to complete a questionnaire that measures social well-being. Higher numbers indicate more positive well-being. Your results indicate that the average well-being score is 100 points with a standard deviation of 20 points. Use this information to answer problems 1-16 below.Finding Probability under the Normal CurveNote: to report number of people, multiply the proportion by the number of people. Always round people UP to a whole number.

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Description: sub parts 14-16 14. What well-being score represents the 90th percentile?15. What well-being score represents the 50th percentile?16. What well-being score represents the 66th percentile? For your doctoral dissertation, you decide to study the social

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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sub parts 14-16

14. What well-being score represents the 90th percentile?

15. What well-being score represents the 50th percentile?

16. What well-being score represents the 66th percentile?

For your doctoral dissertation, you decide to study the social well-being of 100,000 people. You ask them to complete a questionnaire that measures social well-being. Higher numbers indicate more positive well-being. Your results indicate that the average well-being score is 100 points with a standard deviation of 20 points. Use this information to answer problems 1-16 below.

Finding Probability under the Normal Curve
Note: to report number of people, multiply the proportion by the number of people. Always round people UP to a whole number.

Expert Solution

Step 1

a) Well-being score that represents 90th percentile

$P (x > y) = 0.1 P (\frac{x - 100}{20} > \frac{y - 100}{20}) = 0.1 P (z > \frac{y - 100}{20}) = 0.1 . . . . (1) U \sin g s \tan d a r d n o r m a l d i s t r i b u t i o n t a b l e P (z > 1.28) = 0.1 . . . . . (2) F r o m e q u a t i o n (1) a n d (2) \frac{y - 100}{20} = 1.28 y = 1.28 \times 20 + 100 y = 125.6$

Well being score of 125.6 represents 90th Percentile.

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