Answer:
The probability that the stock market would have a return of -23% or worse on one particular day (as it did on Black Monday) is approximately 0%.
Explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
If the daily returns on the stock market are normally distributed with a mean of .05% and a standard deviation of 1%
This means that

The probability that the stock market would have a return of -23% or worse on one particular day (as it did on Black Monday) is approximately
This is the p-value of Z when X = -23. So



has a p-value of approximately 0. So
The probability that the stock market would have a return of -23% or worse on one particular day (as it did on Black Monday) is approximately 0%.