10*10=100
100*132.71=13271
109.526 + 36.42 equals 145.946
The 99% confidence interval for the true mean is given by:

where:

is the sample mean = 69.7

is the standard deviation = 2.8

is the test statistics = 2.58 for for 99% confidentce interval.
n is the sample size = 772.
Therefore, the 99% confidence interval is:
It is a 1.16% chance the student failed- it is a 98.94% one passed 6/7 passsd- there is a 98.94% probablility it passed!