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azamat
3 years ago
13

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 d

eviation of that data set? Devry course
Mathematics
1 answer:
NeX [460]3 years ago
3 0

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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