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Statistics - Expected Percentage / Standard Deviation

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Assume that within an investment pool of 1,000 mortgages (a mortgage-backed security) there are 562 that are 'under water' - i.e. the current market value is less than the outstanding mortgage balance. Suppose further that 160 mortgages will be randomly chosen from the pool by an investment group (that does not know the exact number that are under water) in order to determine the quality of the pool.

---Find the expected percentage of mortgages that will be found to be 'under water' in the investment group's survey.

---Find and interpret the standard deviation of the percentage of mortgages that will be found to be 'under water' in the investment group's survey.

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The expected percentage and standard deviation in statistics is examined. A complete, neat and step-by-step solution is provided.

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p = 562/1000 = 0.562 and q = 1 - p = 0.438

(a) Expected number of mortgages out of 160 that wil be under water = 160 * 0.562 = ...

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