Question

According to the "January theory," if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in The Wall Street Journal, this theory held for 23 out of the last 31 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is 0.50.

What is the probability that this could occur by chance? (Round the final answer to 4 decimal places.)

Answer 1

Here we have:

trials = 31, p = 0.50, and X 23

binomial probability formula with the binomial coefficient is P(X) = n! •px.(1 – p)n-X X!(n – X)!

where n is the number of trials, p is the probability of success on a single trial, and X is the number of successes. Substituting in values for this problem, n = 31, p = 0.50, and X = 23. P(23) = 31! - 0.5023 - (1 – 0.50)31–23 23!(31 – 23)! Evaluating the expression, we have

P ( 23) = 0.0037 (Round to four decimal place)