Assignment:
The Webster National Bank, a small Midwestern bank is reviewing its service charges and interest paying policies on checking accounts. The bank presently has a total of $5000 checking accounts. The bank has found that the average daily balances on all of its personal checking accounts is $550 with a standard deviation of $150. In addition, the average daily balances have been found to be normally distributed. Listed below are 20 randomly selected accounts.
Account Acct Balances Account Acct Balances Account Acct Balances Account Acct Balances
1 $539 6 $523 11 $535 16 $800
2 $575 7 $569 12 $386 17 $545
3 $700 8 $565 13 $810 18 $559
4 $714 9 $531 14 $550 19 $461
5 $546 10 $402 15 $290 20 $560
1. Determine the mean average balance based upon the sample data.
2. If you were to draw another random sample of 20 observations from the same population, what is the probability that you would find a larger sample mean than the value you calculated in question 1?
3. Webster National Bank conducted some analysis that reveals that approximately 5 percent of its accounts have an average daily balance below $304. Based upon this information, in a randomly drawn sample of 2,000 accounts, what percentage of accounts could be expected to have an average daily balance below $304?
4. Based upon the population data, what percentage of customers carry average daily balances above $800?
5. Based upon the population data, what is the daily balance level that you would expect only 25 percent of the customers to exceed?
6. Based upon the population data, what percentage of customers carry average daily balances blow $200?
7. Based upon the population data, what percentage of customers carry average daily balances between $200 and $700?
8. Webster National Bank has conducted some analysis in consideration of invoking minimum balance requirements because some of its clients maintain unprofitable account balances. If Webster National Bank is considering a minimum account balance of $127, how many customers would be expected to have a balance below this value?
Provide complete and step by step solution for the question and show calculations and use formulas.