According to data collected by the National Oceanic and Atmospheric Administrati

Question

According to data collected by the National Oceanic and Atmospheric Administration, the last time the earth experienced a month in which the average temperature was less than the 20th century average for that month was February, 1985 or 392 months ago. Consider the possibility that this is a just a "hot streak" and that the probability of any given month being hotter than the 20th century average is still 1/2. What is the probability of this outcome given this assumption? Compare your answer to the probability of winning the powerball jackpot: P(Winning Powerball)-1/292, 201, 338 3.4x 10-9 (per play).

Explanation / Answer

Here we have seen the last time in which the average temperature was less than 20th century average is 392 months back.

Herw we can assume that the probability of any given month to have temperatue greater than average is 0.5.so we can take the given problem as binomial problem where in next 392 months, there are no month, in which temerature is lower than the average temperature.

So number of months = 392

Pr(Hot month) = 0.5

Pr(all 392 months are hotter than avergae) = BIN (X = 0 ; 392; 0.5) = 392 C0 (0.5)392 = 9.91 x 10-119

so that is ridiculously low probability even if compared with the probability to win powerball which has an order of 10-9 . So, yes there we can reject the assumption that Probability of any given month being hotter than the 20th century average is 0.5. That means tempeatue is rising.

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