## Unit 2:  Probability

The following contingency table comes from data provided by the World Health Organization. Each column represents a range of combined (both male and female) life expectancy in years, from birth, for a given country. Each row represents a region of the world, as defined by the World Health Organization. The values given in the table represent how many countries in a certain region have a combined life expectancy in the given range. Use the contingency table to answer the following questions.

 50-54.9 55-59.9 60-64.9 65-69.9 70-74.9 75-79.9 80-84.9 Total Africa 7 12 16 7 3 1 0 46 Americas 0 0 1 1 14 15 2 33 Eastern Mediterranean 0 2 4 3 7 6 0 22 Europe 0 0 0 3 12 13 22 50 South-East Asia 0 0 0 6 4 1 0 11 Western Pacific 0 0 1 8 3 4 5 21 Total 7 14 22 28 43 40 29 183

1.      What is the probability that an individual from a randomly selected country has a life expectancy of 70 or more years? Show your work and round your final answer to 4 decimal places. Answer in a sentence.

43/183+40/183+29/183= .6120

2.      What is the probability that an individual from a randomly selected European country has a life expectancy of 70 or more years? Show your work and round your final answer to 4 decimal places. Answer in a sentence.

3.      What is the probability that an individual from a randomly selected African country has a life expectancy of 70 or more years? Show your work and round your final answer to 4 decimal places. Answer in a sentence.

3/46+1/46= .0870

4.      What might be some of the reasons for the difference in the above two probabilities? Give a paragraph answer with complete sentences. If you have done some research for your answer, please indicate where you got your information.

5.      If we randomly select three countries, what is the probability that all three of them have a combined life expectancy of 70 years or more? Show your work and round your final answer to 4 decimal places. Answer in a sentence.

6.      If you randomly select a country which has a combined life expectancy of 70 years or older, what is the probability that it is in the Americas or Europe? Show your work and round your final answer to 4 decimal places. Answer in a sentence.

For the following three problems, suppose we select 1000 individuals via the following process: we randomly select a country, and then randomly select an individual from that country. We repeat that process until we have a sample of 1000 people.

7.      What is the probability that no more than 500 of the 1000 people have a life expectancy of 70 years or older? (Hint: Use the binomial distribution.) Show/explain how you come to your conclusion. Round the probability to four decimal places.

8.      How many of the 1000 individuals would you expect to have a life expectancy of 70 years or older? Show your work and explain your answer. Use complete sentences.

9.      Would it be unusual for only 400 or fewer of the 1000 people to have a life expectancy of 70 years or older? Show work and explain your answer. Use complete sentences.

Interesting Article about Life Expectancy predictions for the U.S.

https://www.cnbc.com/2017/02/22/us-life-expectancy-is-low-and-is-now-projected-to-be-on-par-with-mexico-by-2030.html

Link to the World Health Organization website

http://www.who.int/en/