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  

Google will be a big help to you for this.  http://turner.faculty.swau.edu/mathematics/math241/materials/percentilez/

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