Solve the below:
1. Given that z is a standard normal random variable, compute the following probabilities.
a. p (z = 2.0)
b. p (z ≥ 1.4)
c. p (-1.0 < z < 0.5)
d. p (1.0 < z < 1.2)
2. The time needed to drive from city A to city B is normally distributed with a mean of 180 minutes and standard deviation of 20 minutes.
a. What is the probability that a person will drive from city A to city B in three hours or more?
b. What is the probability that a person will drive from city A to city B in more than 140 minutes?
c. What is the probability that a person will drive from city A to city B in exactly three hours?
d. What is the probability that a person will drive from city A to city B in less than 2.5 hours?