Answer:
The answer is "There are [tex]97.5\%[/tex] of the students pass in the test ".
Step-by-step explanation:
Since a normally distributed random variable, the practical rule states:
About 68% of the metrics are in the 1 default deviation
About 95% of metrics correspond to 2 standard deviations from the average.
About 3 standard deviations of the average represent 99.7% of the measurement.
We have the following in this problem:
Average of 78, the average 9 default.
Calculating the percentage of students that passed the test.
[tex]Above 60\\\\60 = 78 - 2\times 9[/tex]
Therefore 60 is under the average for two standard deviations.
Its normality test is symmetric, so 50% of such observations are below mean and 50% below mean.
Everything was cleared of the 50 percent above.
Of the 50% below, 95% (within 2 known mean deviations) succeeded.
therefore
[tex]p=0.5+0.5 \times 0.95=0.975[/tex]
