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

NormalCdf(-2,2,0,1)=.9545
95.45%

Answer 2

Answer:

95.44% of the data lies between 8 and 16.

Step-by-step explanation:

Since, z score or standard score formula is,

$z=\frac{x-\mu}{\sigma}$

Where,

$\mu$ = mean of the data,

$\sigma$ = standard deviation,

Let X represents a data point,

So, we have to find out,

P( 8 < X < 16),

Since,

$P(8 < X < 16)=P(\frac{8-\mu}{\sigma}< Z< \frac{16-\mu}{\sigma})$

$=P(\frac{8-12}{2}<Z<\frac{16-12}{2})$

$=P(-2<Z<2)$

$=P(Z<2) - P(Z<-2)$

$=0.9772-0.0228$  ( By the z-score table )

$=0.9544$

$=95.44\%$

Hence, 95.44% of the data lies between 8 and 16.