Question

In: Statistics and Probability

An officer of a micro-lending company in a developing country has made eight loans of $100...

  1. An officer of a micro-lending company in a developing country has made eight loans of $100 each. Let Xi be a random variable representing the real rate of return on loan i, i = 1, ..., 8. The real rate of return on loan i is a random variable because a borrower sometimes delays or skips payments, and because inflation during the life of the loan can vary. Assume Xi is approximately normally distributed with mean 0.10, and standard deviation 0.02.  Use 4 decimals in your calculations, then round to the requested number of decimals when you answer.

a. Calculate the probability that loan i will have a real rate of return from 0.09 to 0.11. This probability is  .  TWO DECIMALS.

b.  Continued. Find the symmetric interval (a, b) such that the probability is 0.99 that Xi will fall in this interval. Find the interval that is symmetric around the mean of the distribution of Xi. The value of “a” is  . The value of “b” is  .  THREE DECIMALS.

c. Calculate the probability that the mean of the real rates of return on the loan officer’s eight loans will be from 0.09 to 0.11. This probability is  .  TWO DECIMALS.

d.  Continued. Find the symmetric interval (a, b) such that the probability is 0.99 that the mean real rate of return will fall in this interval. Find the interval that is symmetric around the mean of the distribution of "Xbar". The value of “a” is  . The value of “b” is  .  THREE DECIMALS.

e. How many loans would the entrepreneur have to make in order for the probability to be at least 0.99 that the mean real rate of return will be from 0.09 to 0.11? Call this number “n”. The value of n is  .  INTEGER (NO DECIMALS).

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orchestra answered 1 year ago
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