• The length of time needed to complete a certain test is normally distributed with mean 74 minutes and standard deviation 12 minutes. Find the probability that it will take less than 88 minutes to complete the test.

• If X is normally distributed with a mean of 30 and a standard deviation of 2, find P(30 X 33.4).

• Suppose that X is normally distributed with a mean of 60 and a standard deviation of 3. What is P(X 64.05)?

• Suppose that x is normally distributed with a mean of 50 and a standard deviation of 4. What is P(x 57.80)?

• Suppose that x is normally distributed with a mean of 20 and a standard deviation of 6. What is P(13.82 x 29.18)?

• At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 76 and a standard deviation of 14. The scores on the calculus final are also approximately normally distributed, with a mean of 74 and a standard deviation of 15. A student scored 79 on the chemistry final and 81 on the calculus final. Relative to the students in each respective class, in which subject did the student do better?

• Find a value of c so that P(Z c) = 0.76.