A set of quiz scores has a mean of 78 and a standard deviation of 9. Using a common grading scale where 60 and above is a passing score, what percentage
of the students passed this test?
Explain your answer in terms of the 68-95-99.7 rule.

95%

Step-by-step explanation:

Given that :

Mean score, μ = 78 ; Standard deviation, σ = 9

To obtain the percentage of student that passed Given that, the average passing score is 60 and above, using the empirical rule :

Recall :

68% = Lies within 1 standard deviation of the mean

95% = Lies within 2 standard deviation of the mean

99.7% = Lies within 3 standard deviation of the mean

A score of 60 and above ;

Number of standard deviations

Z = (x - mean) / standard deviation

Z = (60 - 78) / 9 ;

Z = - 18/9

Z = - 2

Hence, this score lies within 2 standard deviations of the mean.

Hence, percentage of students who passed the test is 95%

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