+118735 
+118735 The SAT mathematics scores (1,664,479 students) in 2012 are approxiimately normally distributed with a mean of 514 and a standard deviation of 117.
$$\\\mu=514 \qquad \sigma=117$$
a. bob achieved a score of 700 on the test. How many standard deviations away from the mean is his score of 700?
$$\\z=\frac{700-514}{117}\\\\
z=\frac{186}{117}\\\\$$
$${\frac{{\mathtt{186}}}{{\mathtt{117}}}} = {\frac{{\mathtt{62}}}{{\mathtt{39}}}} = {\mathtt{1.589\: \!743\: \!589\: \!743\: \!589\: \!7}}$$
His score is 1.59 standard deviations above the mean.
b. What percentage of those who took the test scored higher than Bob?
http://davidmlane.com/hyperstat/z_table.html
0.0559*100 = 5.59% scored higher
c. What is the cutoff point for the top 5% of scores.
http://stattrek.com/online-calculator/normal.aspx
z=1.645
$$\\1.645=\frac{x-514}{117}\\\\
1.645*117=x-514\\\\
1.645*117+514=x\\\\$$
$${\mathtt{1.645}}{\mathtt{\,\times\,}}{\mathtt{117}}{\mathtt{\,\small\textbf+\,}}{\mathtt{514}} = {\mathtt{706.465}}$$
5% of scores are more than 706
d. Find the 99th percentiles for SAT math scores.
I assume this means what is the cut off for the top 1% of scores.
http://stattrek.com/online-calculator/normal.aspx
crit z = 2.326
$$\\2.326=\frac{x-514}{117}\\\\
2.326*117=x-514\\\\
2.326*117+514=x\\\\$$
$${\mathtt{2.326}}{\mathtt{\,\times\,}}{\mathtt{117}}{\mathtt{\,\small\textbf+\,}}{\mathtt{514}} = {\mathtt{786.142}}$$
1% of scores are greater than 786
e. What is the percentage of students who score between 520 and 695?
http://davidmlane.com/hyperstat/z_table.html
0.4186 = 41.86%
Usually you would have to change these scores to zscores first (using the formula above)
But this site I used allows me to insert what ever mean and standard deviation that I want so I didn't bother.
I hope all that helps 
