1. Suppose, Z follows a standard normal distribution (i.e. a normal distribution with mean 0 and variance 1).
a.) What is the probability that Z is smaller than 1.02?
b.) What is the probability that Z is greater than 0.65?
c.) What is the probability that Z is between -2 and -0.5?
d.) What is the probability that the interval [Z-1, Z+1] contains the value 0?
e.) What is the probability that the interval [Z-1, Z+1] contains the value 2?
f.) What is the probability that the interval [Z-1, Z+3] contains the value 2?
g.) What is the probability that the interval [Z+1, Z+2] contains the value 2?
h.) Suppose you want to construct an interval of the form [Z-h, Z+h] that contains the value
0 with 90% probability. What value of h do you have to choose?
i.) Suppose you want to construct an interval of the form [Z-h, Z+h] that contains the value
0 with 80% probability. What value of h do you have to choose?