Read the case study about WTVX a television station located

Read the case study about WTVX (a television station) located in the top

While reading, keep in mind that this case study is immediately following the chapter on statistics. Also, as a tip for understanding the issue, think of the example of a boy flipping a coin 4 times.  The probability of getting a heads is 50%. What is the chance of getting EXACTLY 2 heads? If you were to use the calculation of the weather forecaster, what would he say?

Upon reading the case, answer the 2 questions. Your answers should be in managerial/memo format; i.e. as if you are sending your results to upper management.

thank you for answering completly the question

o to Favorites Help Case Study WTVX WTVX, Channel 6, is located in Eugene, Oregon, home of the would be phoned in, and they were answered on the spot by Joe. University of Oregon\'s football team. The station was owned Once a 10-year-old boy asked what caused fog, and Joe did an and operated by George Wilcox, a former Duck (University of excellent job of describing some of the various causes. Oregon football player). Although there were other television stations in Eugene, WTVX was the only station that had a high school senior asked Joe what the chances were of getting 15 weatherperson who was a member of the American Meteoro days of rain in the next month (30 days). Joe made a quick calcula- logical Society (AMS). Every night, Joe Hummel would be tion: (70%) × (15 days/30 days)-(70%)(12)-35%. Joe introduced as the only weatherperson in Eugene who was a quickly found out what it was like being wrong in a university member of the AMS. This was George\'s idea, and he believed town. He had over 50 phone calls from scientists, mathemati- that this gave his station the mark of quality and helped with cians, and other university professors, telling him that he had market share. Occasionally, Joe would make a mistake. For example, a 5 made a big mistake in computing the chances of getting 15 days In addition to being a member of AMS, Joe was also the of rain during the next 30 days. Although Joe didn\'t understand most popular person on any of the local news programs. Joe was all of the formulas the professors mentioned, he was determined always trying to find innovative ways to make the weather in to find the correct answer and make a correction during a future teresting, and this was especially difficult during the winter broadcast. months when the weather seemed to remain the same over long periods of time. Joe\'s forecast for next month, for example, was Discussion Questions that there would be a 70% chance of rain every day, and that what happens on one day (rain or shine) was not in any way de pendent on what happened the day before. 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 One of Joe\'s most popular features of the weather report was to invite questions during the actual broadcast. Questions the weather for the next 30 da

Solution

To

The Management,

Sub:- Estimation of chances of 15 days of rain in next 30 days and the opinion about the assumptions.

As per the estimation conducted by Joe, he came up with a chance of 1.06% of having 15 days of rain in next 30 days. In order to support his estimation, Joe has provided the following calculation:-

Chance of rain=70%

Chance of sun=30%

Probability of success =                 n!/r!(n-r)! (pr(qn-r)

N= Number of days = 30

R= number of success =15

P= chance of success0.7

Q= Chance of Failure =0.3

R= 30!/ 15!{0.7}15(0.3)15

R=0.0106 =1.06%

Thus the probability of getting exactly 15 days of rain in next 30 days 1.06%

If we look at Joe’s assumptions concerning the weather for the next 30 days state that what happens on one day (rain or shine) was not in any way dependent on what happened the day before. We can see that Joe’s assumption was there would be a 70% chance of rain every day. We can say that Joe knows more about the weather than the group does. So, it is hard to question his opinion. The group being not familiar with the field of meteorology, we cannot say precisely the basis for those assumptions. Those assumptions may have scientific explanations that the group is not familiar with. Based on Joe’s assumptions, we can say that when there is a Low-Pressure Area today, it will not affect tomorrow’s weather.

But the group based on the observations, that there are perhaps certain conditional probabilities associated with the weather of the day. Let us take as an example the 5-day weather forecast of GMA Weather Central as presented below. The probability of rain on Monday (95% chance) is not the same as the chance of having rain on Sunday (100%) and even the percentage chance of rain for the 5 days were different.

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