Credit card usage is requiring an increasing amount of information from users in order to avoid credit card theft and abuse. For example, an applicant s annual income, among other factors, will dictate their credit limit. It is known that the annual income of last year's American Express Platinum Card applicants in the San Francisco Bay Area follow a normal distribution with a mean of $87,000 and a standard deviation of $10,000. American Express automatically approves Platinum Card applicants whose salary is in the top 15% of all applicants. What is the minimum income required to be automatically approved for a Platinum Card? 7. Suppose you record how long it takes you to get to school over many months and discover that the one-way travel times, in minutes, are approximately normally distributed with a mean of 13.88 minutes and standard deviation of 4 minutes. If your first class is at 10:30 am, what is the latest time you should leave everyday so that you are on time at least 93.7% of the time? 8. Flat screen monitors manufactured by an offshore OEM supplier have life spans which are normally distributed with a mean life of 13,500 hours and a standard deviation of 1,200 hours. Suppose that you are a large buyer of these monitors for your company, which you subsequently sell on the open market, and your company wants to guarantee these monitors for a minimum life span. What should you set the minimum life span to be, if you want no more than 3% of your sales to result in having to provide the customers with new monitors to replace failed ones? How many days of consecutive usage would you be guaranteeing to your customers?