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# Statistics: Normal distribution.

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1. In the National Weekly Edition of the Washington Post (December 19-25, 2005), firstStreet, Inc. advertised an atomic digital watch from LaCrosse Technology. It is radio-controlled and maintains its accuracy by reading a radio signal from a WWVB radio signal from Colorado. It neither loses nor gains a second in 20 million years. It is powered by a 3-volt lithium battery expected to last three years. Suppose the life of the battery has a standard deviation of 0.3 years and is normally distributed.
a. Determine the probability that the watch's battery will last longer than 3 and 1/2 years.
b. Calculate the probability that the watch's battery will last more than 2.75 years.
c. Compute the length-of-life value for which 10% of the watch's batteries last longer.

2. A global financial institution transfers a large data file every evening from offices around the world to its New York City 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?