Assume a data set is normally distributed with mean 106 and standard deviation 35. If the data set contains 400 data values, approximately how many of the data values will fall within the range 36 to 176?

Question

anonymous · Answer

$$\begin{align*}
P(36<X<176)&=P\left(\frac{36-106}{35}<Z<\frac{176-106}{35}\right)\
&=P(-2<Z<2)\
&=P(Z<2)-P(Z<-2)
\end{align*}$$

anonymous · Answer

Once you find this probability, you multiply it by the sample size to determine the frequency. That is, multiplying the result by 400 will give you the number of data values that fall in the desired range.