question archive High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam
High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 11 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
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Answer:
a student have to score 1.23 standard deviation above the mean to be publicly recognized.
Step-by-step explanation
we have P(X>x)=0.11
this means top 11% of the normal distribution
from z table
P(Z>z)=0.11 or
P(Z<z)=0.89
z=1.23
we know that z=(x-u)/sd means how many standard deviation away is x from mean u.
so here, a student have to score 1.23 standard deviation above the mean to be publicly recognized.
