Question HelpIn a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. Tmean response was 5.3 with a standard deviation of 2.5.(a) What response represents the 85th percentile?(b) What response represents the 62nd percentile?(c) What response represents the first quartile?(a) The response that represents the 85th percentile is(Round to two decimal places as needed.)Enter your answer in the answer box and then click Check Answer.2 partsremainingClear AllCheck AnswerP Type here to search4:00 PM11/2/2020DI

Name: Question HelpIn a recent study on world happiness, participants were
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Description: Question HelpIn a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. Tmean response was 5.3 with a st

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Step 1

According to the sum, in a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10 where 0 represents the worst possible life and 10 represents the best.

The mean response was 5.3 and s.d. was 2.5.

Let X be a random variable representing the current lives of the participants.

So, $X ~ N (5.3, 2 . 5^{2})$

Z= $\frac{X - μ}{σ} ~ N (0, 1)$

Step 2

a. The 85^th percentile is:

P(X $\leq x) = 0.85$

$P (\frac{X - 5.3}{2.5} \leq \frac{x - 5.3}{2.5}) = 0.85$

P(Z $\leq \frac{x - 5.3}{2.5}) = 0.85$

x=5.3+(2.5 $\times ϕ^{- 1} (0.85))$

=5.3+(2.5*1.036)

=7.89.

b. The 62^nd percentile :

P(X $\leq x) = 0.62$

$P (\frac{X - 5.3}{2.5} \leq \frac{x - 5.3}{2.5}) = 0.62$

P(Z $\leq \frac{x - 5.3}{2.5}) = 0.62$

x=5.3+(2.5 $\times ϕ^{- 1} (0.62))$

=5.3+(2.5*0.305)

=6.0625

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