Loan Amount Type Region $ 33,000.00 Consumer 1 $ 30,500.00 Commercial 1 $ 84,500.00 Commercial 2 $ 110,500.00 Commercial 3 $ 21,500.00 Commercial 3 $ 59,500.00 Commercial 4 $ 48,500.00 Real Estate 1 $ 57,000.00 Commercial 2 $ 116,000.00 Commercial 3 $ 89,500.00 Consumer 1 $ 40,000.00 Consumer 1 $ 117,500.00 Real Estate 1 $ 78,500.00 Commercial 1 $ 76,000.00 Consumer 1 $ 90,000.00 Commercial 1 $ 19,000.00 Commercial 1 $ 72,500.00 Consumer 1 $ 57,000.00 Real Estate 1 $ 102,500.00 Real Estate 2 $ 36,000.00 Commercial 1 $ 123,500.00 Consumer 1 $ 9,000.00 Consumer 1 $ 31,000.00 Commercial 4 $ 5,500.00 Consumer 2 $ 29,000.00 Commercial 2 $ 82,000.00 Real Estate 1 $ 10,500.00 Consumer 4 $ 72,000.00 Commercial 3 $ 67,000.00 Commercial 4 $ 6,500.00 Consumer 1 $ 28,500.00 Commercial 4 $ 113,500.00 Consumer 1 $ 99,000.00 Real Estate 3 $ 93,500.00 Real Estate 3 $ 102,000.00 Consumer 4 $ 94,000.00 Consumer 2 $ 89,500.00 Commercial 1 $ 66,500.00 Commercial 3 $ 22,000.00 Commercial 1 $ 107,000.00 Consumer 3 $ 65,000.00 Commercial 1 $ 109,000.00 Commercial 1 $ 118,000.00 Real Estate 1 $ 5,500.00 Commercial 1 $ 124,500.00 Commercial 2 $ 12,000.00 Commercial 2 $ 86,000.00 Consumer 1 $ 113,500.00 Consumer 4 $ 93,500.00 Commercial 1 $ 6,000.00 Commercial 1 $ 108,500.00 Consumer 1 $ 63,500.00 Commercial 4 $ 24,500.00 Consumer 1 $ 85,500.00 Commercial 1 $ 95,000.00 Real Estate 3 $ 89,000.00 Real Estate 3 $ 83,000.00 Real Estate 3 $ 98,500.00 Consumer 3 $ 98,000.00 Commercial 1 $ 57,000.00 Commercial 1 $ 79,000.00 Commercial 3 $ 36,000.00 Commercial 3 $ 78,000.00 Consumer 1 $ 50,000.00 Commercial 2 $ 98,000.00 Consumer 2 $ 87,000.00 Consumer 3 $ 22,000.00 Real Estate 2 $ 70,000.00 Consumer 1 $ 36,500.00 Consumer 4 $ 117,000.00 Real Estate 3 $ 66,000.00 Commercial 2 $ 84,000.00 Commercial 3 $ 118,500.00 Consumer 3 $ 70,000.00 Real Estate 1 $ 125,000.00 Consumer 1 $ 99,000.00 Commercial 3 $ 32,500.00 Consumer 1 $ 15,000.00 Consumer 1 $ 4,000.00 Commercial 3 $ 115,000.00 Commercial 3 $ 108,500.00 Commercial 4 $ 101,000.00 Commercial 4 $ 120,000.00 Commercial 4 $ 48,000.00 Commercial 2 $ 94,000.00 Consumer 2 $ 86,000.00 Commercial 3 $ 57,500.00 Consumer 2 $ 16,000.00 Consumer 1 $ 40,500.00 Consumer 1 $ 42,000.00 Commercial 3 $ 117,000.00 Commercial 3 $ 18,500.00 Commercial 3 $ 44,000.00 Commercial 2 $ 59,000.00 Commercial 1 $ 105,000.00 Consumer 3 $ 101,000.00 Consumer 1 $ 12,000.00 Consumer 1 $ 8,500.00 Commercial 1 $ 9,000.00 Commercial 1 $ 33,000.00 Consumer 1 $ 16,000.00 Commercial 1 $ 123,000.00 Commercial 3 $ 64,500.00 Consumer 3 $ 71,000.00 Commercial 1 $ 63,500.00 Commercial 4 $ 50,000.00 Consumer 1 $ 109,000.00 Commercial 3 $ 92,000.00 Commercial 2 $ 30,000.00 Consumer 2 $ 79,000.00 Commercial 1 $ 32,500.00 Commercial 1 $ 37,500.00 Commercial 3 $ 16,500.00 Consumer 3 $ 77,500.00 Consumer 3 $ 58,000.00 Real Estate 3 $ 15,000.00 Consumer 4 $ 40,000.00 Consumer 3 $ 53,500.00 Commercial 3 $ 74,000.00 Commercial 4 $ 3,500.00 Commercial 1 $ 36,000.00 Commercial 3 $ 16,000.00 Commercial 2 $ 62,000.00 Commercial 3 $ 39,500.00 Commercial 2 $ 95,500.00 Commercial 1 $ 44,500.00 Commercial 3 $ 81,500.00 Consumer 1 $ 3,500.00 Commercial 3 $ 56,500.00 Commercial 3 $ 106,000.00 Real Estate 1 $ 17,500.00 Consumer 1 $ 75,500.00 Commercial 1 $ 114,500.00 Consumer 4 $ 45,000.00 Consumer 1 $ 9,000.00 Commercial 2 $ 112,500.00 Real Estate 2 $ 40,000.00 Commercial 4 $ 82,000.00 Commercial 3 $ 16,000.00 Consumer 3 $ 109,500.00 Commercial 4 $ 112,000.00 Real Estate 2 $ 7,500.00 Commercial 3 $ 43,000.00 Commercial 2 $ 90,500.00 Commercial 1 $ 94,000.00 Commercial 3 $ 56,500.00 Real Estate 1 $ 25,500.00 Commercial 1 $ 89,000.00 Commercial 3 $ 6,500.00 Commercial 3 $ 9,500.00 Commercial 3 $ 89,000.00 Commercial 3 $ 56,500.00 Consumer 1 $ 6,500.00 Commercial 3 $ 95,500.00 Commercial 3 $ 23,500.00 Commercial 3 $ 122,000.00 Commercial 1 $ 12,500.00 Real Estate 3 $ 114,500.00 Commercial 4 $ 39,000.00 Consumer 1 $ 91,000.00 Commercial 2 $ 121,500.00 Consumer 4 $ 65,000.00 Real Estate 4 $ 24,500.00 Real Estate 2 $ 120,500.00 Consumer 2 $ 123,000.00 Real Estate 4 $ 8,000.00 Consumer 2 $ 123,500.00 Consumer 1 $ 59,000.00 Commercial 3 $ 108,500.00 Consumer 2 $ 31,000.00 Commercial 3 $ 111,000.00 Consumer 3 $ 89,000.00 Commercial 4 $ 73,000.00 Commercial 2 $ 27,500.00 Commercial 1 $ 118,000.00 Consumer 1 $ 46,500.00 Consumer 1 $ 6,000.00 Consumer 2 $ 102,500.00 Real Estate 3 $ 90,500.00 Commercial 2 $ 106,500.00 Consumer 2 $ 81,000.00 Real Estate 3 $ 65,000.00 Real Estate 4 $ 57,000.00 Real Estate 2 $ 112,500.00 Commercial 1 $ 39,000.00 Real Estate 1 $ 64,500.00 Commercial 2 $ 22,500.00 Commercial 3 $ 49,000.00 Consumer 1 $ 91,000.00 Commercial 1 $ 35,000.00 Commercial 3 $ 112,500.00 Commercial 2 $ 107,500.00 Commercial 1 $ 31,000.00 Consumer 2 $ 75,500.00 Commercial 1 $ 105,500.00 Consumer 1 $ 125,000.00 Real Estate 3 $ 74,000.00 Real Estate 2 $ 59,000.00 Commercial 3 $ 31,500.00 Commercial 3 $ 82,500.00 Commercial 2 $ 86,500.00 Commercial 2 $ 10,000.00 Commercial 2 $ 52,500.00 Consumer 2 $ 73,000.00 Commercial 1 $ 58,500.00 Consumer 2 $ 31,500.00 Commercial 2 $ 41,000.00 Consumer 3 $ 15,500.00 Consumer 1 $ 7,000.00 Consumer 3 $ 41,500.00 Commercial 2 $ 39,000.00 Commercial 2 $ 35,000.00 Consumer 3 $ 86,000.00 Commercial 4 $ 94,500.00 Consumer 1 $ 119,000.00 Real Estate 1 $ 63,500.00 Real Estate 3 $ 40,500.00 Commercial 3 $ 17,500.00 Commercial 1 $ 91,000.00 Commercial 1 $ 23,500.00 Commercial 1 $ 102,500.00 Real Estate 2 $ 73,500.00 Commercial 3 $ 111,000.00 Commercial 1 $ 20,000.00 Consumer 1 $ 21,500.00 Commercial 3 $ 29,000.00 Real Estate 2 $ 93,000.00 Real Estate 1 $ 40,500.00 Commercial 2 $ 66,500.00 Commercial 1 $ 11,000.00 Real Estate 1 $ 90,000.00 Consumer 3 $ 76,000.00 Consumer 4 $ 21,000.00 Commercial 1 $ 69,000.00 Commercial 2 $ 81,500.00 Real Estate 2 $ 45,000.00 Real Estate 4 $ 107,500.00 Real Estate 3 $ 64,500.00 Consumer 4 $ 66,500.00 Commercial 2 $ 69,500.00 Commercial 4 $ 83,500.00 Consumer 1 $ 74,000.00 Consumer 1 $ 45,000.00 Commercial 3 $ 79,500.00 Commercial 3 $ 66,000.00 Real Estate 1 $ 21,500.00 Consumer 3 $ 105,000.00 Consumer 2 $ 19,500.00 Real Estate 1 $ 21,500.00 Commercial 1 $ 12,000.00 Commercial 1 $ 110,500.00 Commercial 3 $ 112,000.00 Commercial 3 $ 60,000.00 Commercial 2 $ 34,000.00 Real Estate 2 $ 54,000.00 Commercial 2 $ 45,000.00 Commercial 1 $ 9,000.00 Real Estate 3 $ 123,000.00 Commercial 1 $ 85,000.00 Commercial 4 $ 110,500.00 Real Estate 3 $ 12,500.00 Commercial 3 $ 106,500.00 Real Estate 1 $ 71,500.00 Consumer 3 $ 5,500.00 Commercial 4 $ 23,000.00 Real Estate 1 $ 33,000.00 Consumer 1 $ 18,500.00 Commercial 1 $ 112,500.00 Commercial 4 $ 64,500.00 Real Estate 3 $ 4,500.00 Consumer 2 $ 122,500.00 Consumer 1 $ 105,000.00 Commercial 3 $ 69,500.00 Real Estate 3 $ 115,500.00 Consumer 3 $ 64,000.00 Consumer 1 $ 17,500.00 Consumer 3 $ 6,500.00 Commercial 1 $ 98,500.00 Real Estate 1 $ 11,500.00 Consumer 1 $ 27,000.00 Consumer 4 $ 30,500.00 Real Estate 1 $ 25,000.00 Real Estate 4 $ 124,000.00 Consumer 1 $ 33,000.00 Consumer 1 $ 14,500.00 Consumer 1 $ 77,500.00 Consumer 4 $ 112,000.00 Real Estate 2 $ 8,500.00 Consumer 3 $ 71,000.00 Real Estate 3 $ 63,500.00 Consumer 4 $ 68,000.00 Real Estate 2 $ 11,500.00 Consumer 1 $ 118,500.00 Commercial 1 $ 72,000.00 Consumer 3 $ 92,500.00 Commercial 3 $ 56,500.00 Consumer 3 $ 83,500.00 Consumer 1 $ 91,000.00 Commercial 1 $ 122,000.00 Commercial 2 $ 23,000.00 Commercial 1 $ 38,500.00 Commercial 1 $ 45,500.00 Consumer 3 $ 101,000.00 Consumer 1 $ 44,000.00 Commercial 2 $ 76,500.00 Consumer 2 $ 95,000.00 Commercial 4 $ 62,000.00 Consumer 1 $ 96,000.00 Commercial 1 $ 33,000.00 Commercial 2 $ 75,500.00 Consumer 1 $ 18,500.00 Consumer 1 $ 56,000.00 Consumer 1 $ 81,500.00 Real Estate 3 $ 120,500.00 Real Estate 1 $ 65,000.00 Commercial 3 $ 66,500.00 Consumer 1 $ 7,500.00 Commercial 3 $ 42,500.00 Consumer 1 $ 91,000.00 Commercial 1 $ 16,500.00 Commercial 1 $ 97,000.00 Commercial 2 $ 103,000.00 Commercial 2 $ 76,500.00 Consumer 4 $ 44,500.00 Consumer 1 $ 72,500.00 Consumer 1 $ 20,000.00 Consumer 1 $ 6,000.00 Commercial 3 $ 17,000.00 Real Estate 4 $ 36,000.00 Commercial 1 $ 49,000.00 Consumer 3 $ 70,500.00 Commercial 4 $ 96,000.00 Commercial 1 $ 72,500.00 Consumer 2 $ 96,500.00 Commercial 1 $ 89,000.00 Real Estate 3 $ 109,500.00 Real Estate 2 $ 97,500.00 Commercial 2 $ 86,500.00 Commercial 1 $ 82,500.00 Real Estate 1 $ 43,500.00 Consumer 3 $ 32,000.00 Real Estate 2 $ 73,500.00 Commercial 3 $ 46,000.00 Commercial 1 $ 124,000.00 Consumer 3 $ 41,000.00 Consumer 3 $ 19,000.00 Commercial 1 $ 61,500.00 Real Estate 3 $ 37,500.00 Consumer 1 $ 32,000.00 Real Estate 2 $ 98,500.00 Commercial 3

Part 1

1. Construct a frequency histogram for the dollar value of loans made last year. Use 0 as the smallest value and group by 15,000.
2. Use your frequency distribution to construct a histogram. Does the population distribution appear to be normally distributed?
3. Compute the population mean of the loan data.
4. Compute the population standard deviation of the loan data.
5. What is the smallest sample size you can use such that according to the Central Limit Theorem, you can use a normal distribution for your sampling distribution for the mean?
6. Use that smallest sample size from the Central Limit Theorem to create random sample from the population of loan amounts. use the Data Analysis TookPak and find the Sampling command. Show this (e.g. in the spreadsheet), don't just say a number.
7. Calculate the sample mean from your random sample.
8. Find the sampling error.
9. Using your sample size, what is the smallest and largest value your sampling error could have been.
10. Use the normal distribution to calculate the probability you would get your sample mean or something smaller and the probability that you would get your sample mean or larger. Use Excel for making your calculations. If you use the Excel calculator, save and submit it with your work. NOTE: pretend the population is very large here (and not the 350 given) so there is no need for the population correction factor. We are doing this since most of the time in business we have large data sets, and it is unnecessary. TIP: Ask yourself, what is the mean and standard deviation of the sampling distribution with the sample size you are using.

Part 2

1. Compute the proportion of loans classified as commercial loans out of the 350 listed in the file.
2. It is believed that at least half of all loans are classified as commercial. Use this list of 350 as a sample of all banking loans from last year (think all banks) and find the probability you would get the proportion you do from this sample of 350 if the population proportion, p, is 50%. Use the following as a guide:

• 1. Is the 350-sample size less than 5% of the population of all loans of all banks?
  2. Is n*p>5 and n*(1-p)>5?
  3. Can you use the normal distribution?
  4. Calculate the probability of getting your sample proportion of commercial loans (what you calculated in #1) or something smaller in Excel using the normal distribution. Show your work.