High School

the combined sat scores for the students at a local high school are normally distributed with a mean of 1550 and a standard deviation of 291. the local college includes a minimum score of 1783 in its admission requirements. what percentage of students from this school earn scores that satisfy the admission requirement? p(x > 1783)

Answer :

The percentage of students that will score higher than 1082 is 8.0962668276439%

We can use the normalcdf function in Python to calculate the probability that a standard normal variable will be less than x.

Python

import math

def normal_cdf(x, mean, stddev):

"""

Returns the probability that a standard normal variable will be less than x.

"""

return (1.0 + math.erf((x - mean) / (stddev * math.sqrt(2.0)))) / 2.0

def get_percentage(x, mean, stddev):

"""

Returns the percentage of students that will score lower than x.

"""

cdf = normal_cdf(x, mean, stddev)

percentage = 100 * cdf

return percentage

mean = 1489

stddev = 291

minimum_score = 1082

percentage = get_percentage(minimum_score, mean, stddev)

print("The percentage of students that will score higher than {} is {}%".format(minimum_score, percentage))

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The output of the code is:

The percentage of students that will score higher than 1082 is 8.0962668276439%

Therefore, 8.096% of the students from this school will earn scores that satisfy the admission requirement.

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The combined SAT scores for the students at a local high school are normally distributed with a mean of 1489 and a standard deviation of 291. The local college includes a minimum score of 1082 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement? P(X > 1082).