Question

A set of data with a mean of 45 and a standard deviation of 8.3 is normally distributed. Find the value that is –2 standard deviations away from the mean.

Answer 1

Answer: 28.4

Explanation:

Given : A set of data with a mean of
`\mu= 45`and a standard deviation of
`\sigma=8.3` is normally distributed.

Now, the value that is –2 standard deviations away from the mean is given by :-

`x=\mu-2\sigma\\\\\Rightrrrow\ x=45-2(8.3)\\\\\Rightarrow\ x=45-16.6\\\\\Rightrrrow\ x=28.4`

Hence, the value that is –2 standard deviations away from the mean. = 28.4

Answer 2

45+8.3 = 53.3

45 - (2(8.3)) = 28.4

The value is 28.4 that is –2 standard deviations away from the mean.