Question 1.

a) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. What is the value of Z ? (Explain/show how you obtain your answer.) (7 pts.)

b) For some value of Z, the probability that a standard normal variable is below Z is 0.2090. What is the value of Z ? (Explain/show how you obtain your answer.) (7 pts.)

c) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3340. What is the value of Z ? (Explain/show how you obtain your answer.) (6 pts.)

Question 2. Suppose we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute.

a) What is the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes? (Explain/show how you obtain your answer.) (7 pts.)

b) What is the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot? (Explain/show how you obtain your answer.) (7 pts.)

c) What is the point in the distribution in which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot? (Explain/show how you obtain your answer.) (6 pts.)