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

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=

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

That is

Since x is always positive ( being standard deviation),

Hence  

We will get same value with 62.5 as well.

Hence standard deviation of data set is 2.5.

answer by yourhope:

hi! : )

a farmer that lived in ancient egypt would most likely be barried in the sand, in the desert!

: )