obtain bounds which will include 95% of the downtime of all the customers

A manufacturer of a particular type of computer system is interested in improving its customer support services. As a first step, its marketing department has been charged with the responsibility of summarizing the extent of customer problems in terms of system failures. Over a period of six months, customers were surveyed and the amount of downtime (in minutes) due to system failures they had experienced during the previous month was collected. The average downtime was found to be 25 minutes and a variance of 144. If it can be assumed that downtime is normally distributed:

 

(a) obtain bounds which will include 95% of the downtime of all the customers;

(b) obtain the bound above which 10% of the downtime is included.

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