According to a Salary Survey Study, the average base salary for a brand manager in Houston, Texas, is $89,250 and the average base salary for a brand...

 According to a Salary Survey Study, the average base salary for a brand manager in Houston, Texas, is $89,250 and the average base salary for a brand manager in Los Angeles, California, is $99,500. Assume that salaries are normally distributed, the standard deviation for the salaries brand managers in Houston is $21,325, and the standard deviation for brand managers in Los Angeles is $19,675.

1. What is the probability that a brand manager in Houston has a base salary in excess of $112,150?  [4 points]
2. What is the probability that a brand manager in Los Angeles has a base salary in excess of $97,175 but less than $105,825?  [5 points]
3. What is the probability that a brand manager in Houston has a base salary of less than $81,750?  [3 points]
4. How much would a brand manager Mr. John Roberts in Los Angeles have to make in order to have a salary higher than 96.5% of the brand managers in Houston?  [4 points]
5. What percentage of brand managers in LA earns a salary that is higher than what Mr. John Roberts earns (from part d) above?