1. 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.)

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.)

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.)

2. A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes.

a) What proportion of customers having to hold more than 4.5 minutes will hang up before placing an order? (Explain/show how you obtain your answer.)

b) What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order? (Explain/show how you obtain your answer.)

c) Find the waiting time at which only 10% of the customers will continue to hold. (Explain/show how you obtain your answer.)