If the mean is 382 and standard deviation is 97 then according to empirical rule 50% students scored between 285 and 479 on the exam.
Given mean of 382 and standard deviation of 97.
We have to calculate the percentage of students scored between 285 and 479 on the exam.
Percentage is a number or ratio that is expressed in terms of 100.
We have to use z statistic in this question.
z=X-μ/σ
where μ is mean and
σ is standard deviation
from 285 to 382
z=285-383/97
=-1
p value =0.1587.
From 382 to 479
z=479-382/97
=97/97
=1
p value =0.3413
Total probability from 285 to 382 is 0.3413+0.1587=0.5
Percentage=5/10*100
=50%
Hence the percentage of students scored between 285 and 479 is 50%.
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