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Mathematics 18 Online
OpenStudy (howard-wolowitz):

The average time it takes a loaf of bread to rise is 2.4 hours with a standard deviation of 0.6! What is the z-score of a loaf that takes 3.6 hours to rise

OpenStudy (howard-wolowitz):

@Why_Study_Alone

OpenStudy (michele_laino):

by definition, such quantity, is given by the subsequent formula: \[z = \frac{{3.6 - 2.4}}{{0.6}} = ...?\]

OpenStudy (howard-wolowitz):

i get 2

OpenStudy (michele_laino):

that's right!

OpenStudy (howard-wolowitz):

Consider the lengths of alligators to be { 18.7, 12.3, 18.6, 16.4, 15.7, 18.3, 15.8, 14.9, 17.6, 16.4, 16.7, 17.8, 16.2, 13.8, 15.2, 14.7, 13.2, 15.8, 14.6, 16.6, 16.2, 18.1, 17.5, 17.3} According to the Empirical Rule, 68% of the data should fall between what two numbers? A. 12.78 and 16.4 B. 13 and 16 C. 14.5 and 17.9 D. 15.7 and 16.3

OpenStudy (howard-wolowitz):

thats the hard one

OpenStudy (michele_laino):

I'm thinking...

OpenStudy (howard-wolowitz):

yes its quite annoying

OpenStudy (howard-wolowitz):

I know we have to find Standard deviation first

OpenStudy (michele_laino):

here is the step by step procedure: #1 compute the mean value \(\overline{X}\); #2 compute the standard deviation \(\sigma\): the requested interval (68%) is: \[\overline X - \sigma \leqslant x \leqslant \overline X + \sigma \]

OpenStudy (howard-wolowitz):

ok then thats very interesting

OpenStudy (michele_laino):

of course, the standard deviation \(\sigma\), is the standard deviation of the mean

OpenStudy (howard-wolowitz):

it would be C

OpenStudy (howard-wolowitz):

I think

OpenStudy (michele_laino):

I don't know, since I didn't such computations

OpenStudy (howard-wolowitz):

17.87726

OpenStudy (howard-wolowitz):

14.4897

OpenStudy (michele_laino):

did you use the standard deviation of the mean, please?

OpenStudy (howard-wolowitz):

yes

OpenStudy (howard-wolowitz):

like this: compute xbar - SD and xbar + SD

OpenStudy (michele_laino):

in that case, I think that your answer is correct!

OpenStudy (michele_laino):

please remember that the standard deviation of the mean, is the standard deviation from your data \(\sigma\) divided by \(\sqrt N\), where \(N=24\) is the number of your data

OpenStudy (howard-wolowitz):

yes I will but hey

OpenStudy (howard-wolowitz):

Awesome! Thank you for your help it means a lot STAY COOL! POUND IT BRUHH

OpenStudy (michele_laino):

:)

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