The grades on the last math exam had a mean of 88%. Assume the population of grades on math exams is known to be normally distributed with a standard deviation of 6. What percent of students earn a score between 72% and 90%?

Question

ganeshie8 · Answer

start by finding the zscores for both observations

anonymous · Answer

How? My lessons are not very explanitory.

ganeshie8 · Answer

$\large     Zscore =  \frac{\text{observation  -  mean}}{\text{standard deviation}}$

ganeshie8 · Answer

you're given :
mean = 88
standard deviation = 6

anonymous · Answer

Ok, so 14.6?

ganeshie8 · Answer

Zscore for 72 =   $\large     \frac{72-88}{6} = ?$


Zscore for 90 =   $\large     \frac{90-88}{6} = ?$

anonymous · Answer

-2, and 0.33?

ganeshie8 · Answer

you should get :

Zscore for 72 = -2.67
Zscore for 90 = 0.33

ganeshie8 · Answer

next, find the corresponding areas

ganeshie8 · Answer

knw how to grab areas for zscore from zscore table ?

anonymous · Answer

Assume that I do not know how to do any of this, because I don't.

ganeshie8 · Answer

okay, its going to be very easy

ganeshie8 · Answer

http://www.math.upenn.edu/~chhays/zscoretable.pdf

ganeshie8 · Answer

^^thats the zscore table

ganeshie8 · Answer

area for zscore of -2.67  =   $0.0038$
area of zscore of 0.33 =  $0.6293$

ganeshie8 · Answer

see if u can figure out how i got above areas from zscore table

ganeshie8 · Answer

So, the percent of students earn a score between 72% and 90% =   0.6293 - 0.0038 = 0.6255 = 62.55%

ganeshie8 · Answer

let me knw if smthng doesnt make sense...

anonymous · Answer

I tried so hard to understand that table in my lesson, and honestly It looks like spanish.....

ganeshie8 · Answer

hahah let me explain u quick

ganeshie8 · Answer

like any table,
it has rows and columns

anonymous · Answer

Yes?

ganeshie8 · Answer

$

\begin{array}{|c|c|}
\hline
z&0.09&0.08&0.07&0.06&0.05&0.04&0.03&0.02&0.01&0.00& \
\hline
-3.4&0.0002&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003& \
\hline
-3.3&0.0003&0.0004&0.0004&0.0004&0.0004&0.0004&0.0004&0.0005&0.0005&0.0005& \
\hline

\end{array}
$

ganeshie8 · Answer

interpreting it is very easy :

suppose your zscore is $-3.45$

ganeshie8 · Answer

then, put ur thumb on the row starting with $-3.4$
and put another thumb on the column with $0.05$

ganeshie8 · Answer

$

\begin{array}{|c|c|}
\hline
z&0.09&0.08&0.07&0.06&\color{red}{0.05}&0.04&0.03&0.02&0.01&0.00& \
\hline
\color{Red}{-3.4}&0.0002&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003& \
\hline
-3.3&0.0003&0.0004&0.0004&0.0004&0.0004&0.0004&0.0004&0.0005&0.0005&0.0005& \
\hline

\end{array}
$

ganeshie8 · Answer

you wud get the area  :  $0.0003$

ganeshie8 · Answer

so for zscore of $-3.45$,
the area  is  $0.0003$

ganeshie8 · Answer

see if that makes more or less sense...

anonymous · Answer

More sense haha thank you

ganeshie8 · Answer

good :) 

may i ask u to find the area for zscore of $-3.38$ ?

anonymous · Answer

0.004?

ganeshie8 · Answer

you got it !!

ganeshie8 · Answer

and did u get why we subtracted both areas and concluded answer is 62.55% ?