The graph shown is based on more than 170,000 interviews done by Gallup that too

Question

The graph shown is based on more than 170,000 interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Emotional Health Index Scores (EMIS) are the sample space. We randomly sample one Emotional Health Index Score.

Find the probability that an Emotional Health Index Score is 85.0.

Find the probability that an Emotional Health Index Score is more than 81?

Find the probability that an Emotional Health Index Score is between 80.5 and 82?

Emotional Health Index Score Service - Transportation Manufacturing or production Sales Clerical or office - Installation and repair Construction or mining 3 Manager, executive, or official Business owner Nurse - Professional Farming, fishing, or forestry - Teacher (K-12) Physician 77 78 7980 81 82 838485

Explanation / Answer

We can assume that all the occupations are equally likely to occur in a random sample.

Since all the EMIS scores are lower than 84, the probability that an Emotional Health Index Score is 85.0 = 0

To calculate the probability that an Emotional Health Index Score is more than 81, we see from the chart that 7 out of 14 occupations mentioned have EMIS greater than 81.

So the probability that an EMIS score is gretaer than 81 = 7/14 =0.50

To calculate the probability that an Emotional Health Index Score lies between 80.5 and 82, we see from the chart that 5 out of 14 occupations mentioned have EMIS greater than 81.

So the probability that an Emotional Health Index Score lies between 80.5 and 82 = 5/14 = 0.357

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