Mathematics: In a normally distributed data set a mean of 55 where 99.7% of the data fall between 47.5 and 62.5, what would be the standard deviation of that data set? devry course

In a normally distributed data set a mean of 55 where

Brainly264

12.03.2022

Given that normally distributed data set has a mean of 55 and 99.7% of data fall between 47.5 and 62.5.

Let s be the standard deviation of data set.

Since 99.7% data fall within 3 standard deviations of mean, z-value for 47.5 and 62.5 has an absolute value of 3.

That is |z|=3

But z= $\frac{x-mean}{standard deviation}$

Let us plugin x=47.5 and mean =55 and equate it to 3.

That is $|\frac{47.5-55}{s}| = 3$

$|\frac{-7.5}{s} | =3$

Since x is always positive ( being standard deviation), $|\frac{-7.5}{s} | = \frac{|-7.5|}{s} = \frac{7.5}{s}$

Hence $\frac{7.5}{s}= 3$

$s=\frac{7.5}{3} = 2.5$

We will get same value with 62.5 as well.

Hence standard deviation of data set is 2.5.

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ChasityN8491

06.01.2020

Step-by-step explanation:

There are 2 similar triangles.

EDA and CBA

From that we can get the following proportion.

ED / CB = AD / AB

Filling in the letters we get

6/x = (4 + 3)/3 Combine

6/x = 7/3 Cross Multiply

7x =6*3

7x = 18 Divide by 7

x = 2.57

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