The percentage of students that have scored more than you is 1.39%
<h3>How to illustrate the probability?</h3>
a) Probility that people scored more than Nancy = P(X>1390) = 1- P(X<1390).
Now z= (1390-950)/200
z= 2.2
P(Z<2.2) = 0.9861
So 1- P(X<1390) = 1 - P(Z<2.2) = 1 - 0.9861 = 0.0139
= 1.39 %
Let P1 be the % of people who score below 1100 and P2 be the % of people who scored below 1200
Then % of students between scores of 1100 and 1200 = P2 - P1
Z (X=1100) =0.75 and Z (X=1200) = 1.25
P1 = P(X<1100)= P (Z< 0.75) =0.7734
P2 = P(X<1200)= P (Z< 1.25) =0.8944
Then % of student between score of 1100 and 1200 = P2 - P1 = 0.8944 - 0.7734 = 0.121 = 12.10%
Middle 87.4 % score means that a total of 12.6 % of the population is excluded. That is 6.3% from both sides of the normal curve. So the minimum value for the middle 87.4% will the one which is just above 6.3% of the population i.e. it will have value x such that P(X<x)= .063.
z value (for P(X<x)= .063) = (-1.53)
But Z= (x-u)/ \sigma from here calculating x, x=644
The minimum value of the middle 87.4% score is 644
The maximum value for the middle 87.4 % of the scores will be the one that has 6.3% scores above it, i.e. it will have value x such that P(X>x)= .063.
P(X<x)= 1 -P(X>x)= 1 - 0.063 = 0.937.
Z value (for P(X<x)= 1.53
But Z= (x-u)/ \sigma from here calculating x, x=1256
The maximum value of the middle 87.4% score is 1256
Z value for (X=1432)= 2.41
P(Z<2.41) =0.9920
It means that 99.2 % of scores are less than 1432
So only 0.8% of scores are higher than 1432
but , 0.8% = 165
So 100% = 20625
20625 students took SAT
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