1. A random variable is normally distributed with a mean of 60 and a standard deviation of 9.

a. What is the probability that a randomly selected value from the distribution will be less than 46.5?

b. What is the probability that a randomly selected value from the distribution will be greater than 78?

c. What is the probability that a randomly selected value will be between 51 and 73.5?

2. A global financial institution transfers a large data file every evening from offices around the world to its London headquarters. Once the file is received, it must be cleaned and partitioned before being stored in the company's data warehouse. Each file is the same size and the time required to transfer, clean, and partition a file is normally distributed, with a mean of 1.5 hours and a standard deviation of 15 minutes.

a. If one file is selected at random, what is the probability that it will take longer than 1 hour and 55 minutes to transfer, clean, and  partition the file?

b. If a manager must be present until 85% of the files are transferred, cleaned, and partitioned, how long will the manager need to be there?

c. What percentage of the data files will take between 63 minutes and 110 minutes to be transferred, cleaned, and partitioned?