According to the \"January theory,\" if the stock market is up for the month of

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 29 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.)

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 29 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.

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
P( X = 29 ) = ( 34 29 ) * ( 0.5^29) * ( 1 - 0.5 )^5
= 0.0000162

The probability that January’s performance could correctly predict the year’s performance 29 out of 34 times is 0.00001620

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.