50 !
the scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. jake scored 520 on the test. find the percent of students that scored below jake. round your answer to the nearest whole number. (include a step by step description of the process you used to find that percentage.)

*you will need to find the z-score using the z-score formula, the probability using the table, then change the probability to a percent. (use the z-score table to answer the question.

63% of students

Step-by-step explanation:

Z = (X  -  μ) / σ

Z = 520 - 500 / 60

Z = 0.33

ON THE Z-TABLE

0.33 = 0.6293

62.93%  =  63% of students answer

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!