Question

From historical data, the annual rates of return of S&P 500 stocks from 1985 to 2000 are roughly normally distributed.  The mean is 9.4%, and the standard deviation is 18.25%.  Treating the next 10 years as a simple random sample. What is the probability that the mean annual rate of return is greater than 3% (the current inflation rate)?  Round to 3 decimal places

Answer 1

From historical data, the annual rates of return of S&P 500 stocks from 1985 to 2000 are roughly normally distributed.

The mean is 9.4% and the standard deviation is 18.25%.

Now, we take the next 10 years as a sample.

So, the mean return of these 10 years, would follow normal distribution with mean 9.4 and standard deviation of

We have to find the chance that this mean annual rate of return is more than 3%.

So, if X be the random variable denoting the mean, then X follows normal with mean 9.4 and standard deviation of 5.7712.

So, we have to find

Where, phi is the distribution function of the standard normal variate.

From the standard normal table, it becomes

So, the required probability, that the mean annual return would be more than 3%, is 0.867.