Help regarding z-scores and probabilities?

#1
Can you help me understand how to do these 3 problems? Be specific, please.
Here is my homework, word for word:


Here we are given the probability, say .9 and we find the values of the random variable (-a and a) that determine a probability of .9 on a standard normal distribution.

Remember the solution to these problems make extensive use of the symmetry of the standard normal distribution about the mean. As we did in class, first using the given probability, determine the probability in each of the tails. Then use invnorm to determine the high and low values of the random variable.

So:

A random variable z is normally distributed with mean μ=0 and standard deviation σ=1. For each of the following cases what is the value of the random variable that gives the required probability? Calculate the value to four decimal places.

a. P( -a < z < a) = .9







b. P( -a < z < a) = .95






For this case include a sketch of the distribution that shows the values of the random variable, the area that determines the required probability (.95), and the probability in each of the tails.

c. P( -a < z < a) = .99