Scores on a university exam are normally distributed with a mean of 78 and a standard deviation of 8. the professor teaching the class declares that a score of 70 or higher is required for a grade of at least “
c.” using the 68-95-99.7 rule, what percent of students failed to earn a grade of at least “c”?

Question

10-02-2017
Mathematics

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Scores on a university exam are normally distributed with a mean of 78 and a standard deviation of 8. the professor teaching the class declares that a score of 70 or higher is required for a grade of at least “
c.” using the 68-95-99.7 rule, what percent of students failed to earn a grade of at least “c”?

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mrinconj mrinconj · Answer 1 · 2017-02-17T18:22:02+01:00

Following the empirical rule we have 68% of the data around one standar desviation, we can calculate that interval in this way:
78+/-1*8, using negative: 78-1*8= 70, using positive: 78+1*8= 86, so 68% of student scores is between 70 and 86.
As the mean represents the middle of data, 50% of score is more than 78, and as 68% of data is between 70 and 86 this mean the middle of 68% is between 70 and 78, the other middle of 68% is between 78 and 86, the proportion of student passed is 50%+34%= 84% but they want to know the students failed then 100%-84%= 16% of students failed.