Question: This last question is a bit special. It uses real data from the United Nations, collected in 2016.

The UNITED NATIONS DEVELOPMENT PROGRAMME (UNDP) has invented a tool called the Human Development Index (HDI). It assesses the quality of life.

‘ The Human Development Index (HDI) is a summary measure of average achievement in key dimensions of human development: a long and healthy life, being knowledgeable and have a decent standard of living .’ (UNDP, 2016).

The HDI is calculated using the dimensions described below:

Source: http://hdr.undp.org/en/content/human-development-index-hdi

Life expectancy at birth (in years) is one of the variables used to assess the quality of life. The life expectancy at birth is "the average number of years a newborn child would live if current mortality patterns were to stay the same" (Gapminder, 2016). It is average of the life expectancy for both genders. The range of life expectancies is quite large going from 84.8 years old in Andorra to 48.86 years old in Lesotho.

Let’s consider a life expectancy to be low when it is below 60 years old.

Here are the questions you will try to answer: Knowing that mean of life expectancy is = 72.56 years with a standard deviation = 7.74 years, should the United Nations be concerned and invest money in trying to increase life expectancy? Said differently, what is the probability that a country has a life expectancy below 60 years old?

To answer the questions, you must:

1. Express the problem as a probability of the raw score.
2. Express the problem as a probability of the proper statistic (either Z or t).
3. Draw the graph of the Normal Distribution of Life Expectancy (put a title, label the axis, put the numbers on the axis and shade the area you are looking for). You will be graded on the presentation of the graph.
4. Find the probability (show the calculations).
5. Answer the question in a few sentences: According to your answer in (E), should the United Nations be concerned and therefore invest money in trying to increase life expectancy around the world? There are no right or wrong answers if you justify your reasoning using the probability found above. You will be graded on your argument(s).

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Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document