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).
