You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To repay you, Breck will pay $2,500
at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but
currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7. Breck is
essentially riskless, so you are confident the payments will be made. You regard 8% as an appropriate
rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the
end of each of the final 4 years, that is, what is X?

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.