for mathematicsexpert only

Name_______Lourde Owens_____________

Date______05/26/2016_______________

University of Phoenix Material

INTRODUCTION TO STATISTICAL THINKING

Directions: Complete the following questions. The most important part of statistics is the thought process, so make sure that you explain your answers (and show your work), but be careful with statistics. The following statistics/probability problems may intrigue you and you may be surprised. The answers are not always as you might think.

1. There are 17 people at a party. Explain what the probability is that any two of them share the same birthday. [Show your work]

In probability theory , the birthday problem or birthday paradox concerns the probability that, in a set of randomly chosen people, some pair of them will have the same birthday . By the pigeonhole principle , the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29 ). However, 99.9% probability is reached with just 70 people, and 50% probability with 17 people. These conclusions are based on the assumption that each day of the year (except February 29) is equally probable for a birthday The probability is a 50-50 chance

I think it is beter to calcluate that NO two people have the same birthday. to do that will see that there are 365 days in the year

so P(e)= 1 - P(e’)

meaning (365 days / 365 day ) x (365 days / 365 day ) x (364 days / 365 day )...... (349 days / 365 day )

( 365 – 17 = 348) so we have to reach upto 348 + 1 = 349

= 365 x 365........343 / 365^ 23 = 0.493

(Using permutation it can be written as P(365, 17) / 365^17)

p(e) = 1- P(e')

1-0.685 = 0.315

probability is that any two of them share the same birthday is 31.5%

2. A cold and flu study is looking at how two different medications work on sore throats and fever: [Show your work]

· Sore throat - Medication A: Success rate - 90% (101 out of 112 trials were successful)

· Sore throat - Medication B: Success rate - 83% (252 out of 305 trials were successful)

· Fever - Medication A: Success rate - 71% (205 out of 288 trials were successful)

· Fever - Medication B: Success rate - 68% (65 out of 95 trials were successful)

Analyze the data and explain which one would be the better medication for both a sore throat and a fever.

If we combine the studies medication

A had 306 successes out of 400 which means 306/400 = 76.5%

  B had 317 successes out of 400 which means 317/400 = 79.25%

So if we want to decide which had a better "overall" success rate it would be B.

  This is an example of what is called in statistics "Simpson's Paradox."

3. The United States employed a statistician to examine damaged planes returning from bombing missions over Germany in World War II. He found that the number of returned planes that had damage to the fuselage was far greater than those that had damage to the engines. His recommendation was to enhance the reinforcement of the engines rather than the fuselages. If damage to the fuselage was far more common, explain why he made this recommendation.

Altough the fuselage had the greater amount of damaged planes, the engine is what keeps the planes running. Trying to have 100% of planes with no engine damage would be ideal because without engines the plane cannot fly .

�This is a quote from Wikipedia and not your own work.

Remember, these assignments are designed for you to show your understanding of mathematical theory, not to show how well you can find the answer on line.

Keep in mind it is academic dishonesty when you take words or ideas from the textbook or an outside source and do not provide a correct citation. To avoid this, summarize or paraphrase any outside material in your own words. To paraphrase correctly, change every word from the original source, but retain the original meaning. You need to provide a citation for each sentence where you use borrowed material.

You should have cited this solution and placed the reference on the references page.

0 / 1.33

�If you can explain this solution to me, I will reconsider the points for the problem.

�This leads me to believe you found the solution on line as you would not know this definition from the problem or the readings.

Make sure you present only original thought in your solutions. If you borrow material, properly cite it on the references page.

1 / 1.33

�Good

1.33 / 1.33

Do not forget to submit your paper in APA format (cover page and references page.

2.33 / 4