Question

ABC

ABC, Channel 6, is located in Eugene, Oregon, home of the University of Oregon’s football team. The station was owned and operated by George Wilcox, a former Duck (University of Oregon football player). Although there were other television stations in Eugene, ABC was the only station that had a weatherperson who was a member of the American Meteorological Society (AMS). Every night, Joe Hummel would be introduced as the only weatherperson in Eugene who was a member of the AMS. This was George’s idea, and he believed that this gave his station the mark of quality and helped with market share.

In addition to being a member of AMS, Joe was also the most popular person on any of the local news programs. Joe was always trying to find innovative ways to make the weather interesting, and this was especially difficult during the winter months when the weather seemed to remain the same over long periods of time. Joe’s forecast for next month, for example, was that there would be a 60% chance of rain every day, and that what happens on one day (rain or shine) was not in any way dependent on what happened the day before.

One of Joe’s most popular features of the weather report was to invite questions during the actual broadcast. Questions would be phoned in, and they were answered on the spot by Joe. Once a 10-year-old boy asked what caused fog, and Joe did an excellent job of describing some of the various causes.

Occasionally, Joe would make a mistake. For example, a high school senior asked Joe what the chances were of getting 15 days of rain in the next month (30 days). Joe made a quick calculation:

(60%) x (15 days / 30 days) = (60%) (1/2) = 30%

Joe quickly found out what it was like being wrong in a university town. He had over 50 phone calls from scientists, mathematicians, and other university professors, telling him that he had made a big mistake in computing the chances of getting 15 days of rain during the next 30 days. Although Joe didn’t understand all of the formulas the professors mentioned, he was determined to find the correct answer and make a correction during a future broadcast.

Discussion Questions

1. What are the chances of getting 15 days of rain during the next 30 days?

2. What do you think about Joe’s assumptions concerning the weather for the next 30 days?

Note : Answers should be in Word format

Answer 1

Given

Joe’s forecast for next month,

there would be a 60% chance of rain every day and 40% chance of shine

Total no. of days, n = 30

Total no. of rainy days, r = 15

Probability of raining, p = 60% = 0.60

Probability of Shine, q = 1 - p = 1 - 0.60 = 0.40

(1)

The chances of getting 15 days of rain during the next 30 days can be calculated with the help of bernoulli process through binomial distribution as follows

The chances of getting 15 days of rain during the next 30 days is given by 7.75%

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(2) Joe’s assumptions concerning the weather for the next 30 days are as follows

The suspicions of Joe concerning occurring of the climate in the following 30 days are off base. He is disregarding the awareness of the reality the climate on one specific day has its impact on the resulting day. He has expected that blustery day today would be unessential to the climate for tomorrow. Despite the fact that it is hard to address anticipate these kinds of contingent probabilities yet a guess of such probabilities ought to have been considered while coming at the finish of blustery or bright day. Along these lines we can say that the suppositions of Joe are erroneous.

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