Given that X follows a normal distribution with a mean of 75 and a standard deviation of 5.
To Determine: P(X>80)
Solution:
P(X>a)

P(X>80)



We now go to the standard normal distribution table to look up P(Z>1) and for Z=1.00
We find that

Note, however, that the table always gives the probability that Z is less than the specified value, i.e., it gives us P(Z<1)=0.8413
Therefore:

In percentage

Hence, P(X>80) = 15.87%