Question

The mean of a normally distributed dataset is 12, and the standard deviation is 2.

___% of the data points lies between 8 and 16.

Answer 1

Do you know about z scores?

Answer 2

\[
\mu~~\text{mean}\\
\sigma~~\text{standard deviation}\\
x~~\text{data point}
\]The \(z\) score is given by \[
z=\frac{x-\mu}{\sigma}
\]The \(z\) score is basically just \(x\) translated into the standard normal distribution that has a mean of \(0\) and standard deviation of \(1\).

Answer 3

im confused now?

Answer 4

What have you learned so far?

Answer 5

Do you know how to compute the cumulative normal distribution?