Normal Distributions

The GPA of students in a class are approximately normally distributed with mean 2.7 and standard deviation 0.4.
a) What fraction of the students will possess a GPA better than 3.0?
b) If students possessing a GPA less than 1.9 are dropped from this class, what percentage of the students will be dropped?

Help is appreciated.

alabama14 said:

The GPA of students in a class are approximately normally distributed with mean 2.7 and standard deviation 0.4.
a) What fraction of the students will possess a GPA better than 3.0?
b) If students possessing a GPA less than 1.9 are dropped from this class, what percentage of the students will be dropped?

Help is appreciated.

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Set up your distribution:

X ~ N(2.7, 0.4^2)

a) \(\displaystyle P(X > 3.0) = P(z > \dfrac{x - \mu}{\sigma}) = P(z > \dfrac{3 - 2.7}{0.4}) \)

Find the probability associated with that z-score and convert into fraction.

b) \(\displaystyle P(X < 1.9) = P(z < \dfrac{x - \mu}{\sigma}) = P(z < \dfrac{1.9 - 2.7}{0.4}) \)

Find the probability associated with that z-score and convert into fraction.

Make sure you are getting the correct probability. The probability that you get from your z-table varies from table to table and as such, I rather not say something about how to read the probability as mine could be different from yours.