Question

(You can insert a Desmos graph or a hand-drawn graph.)A set of data has a normal distribution with a mean of 50 and a standard deviation of 10. Draw a normal distribution to model the data below and find the percent of data within each interval.A. All values between 50 to 60.B. All values less than 30.C. All values NOT between 40 and 50

Answer 1

SOLUTION

The graph for the normal distribution is shown below SOLUTION

A. All values between 50 to 60.

Using the Zscore formula we have

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

So, for 50, we have

$\begin{gathered} Z=\frac{50-50}{10} \\ Z=0 \end{gathered}$

For 60, we have

$\begin{gathered} Z=\frac{60-50}{10} \\ =\frac{10}{10} \\ 1 \end{gathered}$

Hence all values between 50 to 60 becomes

P(50Hence the answer is 34.13%

B. All values less than 30.

The Zscore of 30, becomes

$\begin{gathered} Z=\frac{30-50}{10} \\ =\frac{-20}{10} \\ =-2 \end{gathered}$

From the calculator, we have

All values less than 30, becomes

P(x<30) = 0.02275

Hence the answer is 2.275%betwe

C. All values NOT between 40 and 50

Zscore of 40 and 50 becomes

For 50, we know it is 0. For 40, we have \

$\begin{gathered} Z=\frac{40-50}{10} \\ =\frac{-10}{10} \\ =-1 \end{gathered}$

So the probability of all values between 40 and 50 becomes

P(40All values NOT between 40 and 50, becomes

$1-0.34134=0.65866$

Hence the answer becomes 65.866%