Suppose we have a random variable Y, that follows a normal distribution with mean 0 and standard deviation 1.

Please consult the statistics review and the lecture notes for more information.

For each of the following questions, find their probabilities using the z-table from this link: http://www.z-table.com/uploads/2/1/7/9/21795380/8573955.png?759

Hint: Remember that the normal distribution is symmetric and adds up to 1

Hint: Remember that the table below gives Pr(Y z) where z > 0, so you might have to do

some work to get it into a state that you can use the table with.

1. Pr(Y 1.96)
2. Pr(Y > 1.96)
3. Pr(Y > 0)
4. Pr(1.96 Y 1.96)
5. What is 1 Pr(1.96 Y 1.96)? In a hypothesis test, what kind of test (one-tailed, two-tailed) and level would this correspond to?