Automotive dealerships have made recent efforts to reduce the amount of time required to purchase a car. One strategy is to use the Internet to streamline the process by providing prospective buyers with car information. According to J.D. Powers, the average number of minutes to negotiate a deal to purchase a car at the dealership was 60.3 minutes in 2012. Assume the number of minutes to negotiate a deal follows the normal probability distribution with a standard deviation of 17.9 minutes and that these statistics still hold true.

a. What is the probability that a random customer spent

1. Less than 30 minutes negotiating a deal?

2. More than 45 minutes negotiating a deal?

3. Between 50 and 90 minutes negotiating a deal?

4. Between 65 and 85 minutes negotiating a deal?

b. Use Excel or PHStat to confirm the answers in part a.

c. How many minutes of negotiating are in the 35th percentile?