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. Acccording to an article in The Wall Street Journal, this theory held for 24 out of the last 34 years. Suppose there is no truth to this theory, that is, the probability it is either up or down is 0.5. What is the probability this could occur by chance? (Round your answer to 6 decimal places.) Probability

Answer 1

SOLUTION:

From given data,

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 24 out of the last 34 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is 0.5.

What is the probability this could occur by chance? (Round your answer to 6 decimal places.)

Where,

n = 34

x =24

The probability is (1/2) for each year.

p = 1/2 or 0.5
The problem is Binomial with n = 34 and p = 1/2

P(X=x) = ⁿC_x * p^x * (1-p)^n-x Where, ⁿC_x = n! / x!(n-x)!

By substituting the above values,

P(X=24) = ³⁴C₂₄ * (0.5)²⁴ * (1-0.5)^34-24

P(X=24) = 34! / 24!(34-24)!* (0.5)²⁴ * (0.5)¹⁰

P(X=24) = 131128140* (0.5)²⁴ * (0.5)¹⁰

P(X=24) = 0.007633

(or)

P(X = 24) = binomcdf (34,0.5,224) = 0.007633

0.007633  is the probability this could occur by chance .

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