Question

Use the following information to answer the next twelve$12$exercises. 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 are the sample space. We randomly sample one Emotional Health Index Score.

If all occupations are equally likely for a certain individual, what is the probability that he or she will have an occupation with lower than average EHIS$?$

Short answer

The Probability lower than average EHIS is$\frac{1}{2}$.

Step-by-step solution

Definition for probability

The probability of a random event's result is referred to as probability. This term refers to evaluating the likelihood of a particular event that took place.

$\mathrm{P}\left(\mathrm{E}\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{Positive}\mathrm{Outcomes}}{\mathrm{Total}\mathrm{Number}\mathrm{of}\mathrm{Outcomes}}$

$\mathrm{P}\left(\mathrm{E}\right)=\frac{\mathrm{n}\left(\mathrm{E}\right)}{\mathrm{n}\left(\mathrm{S}\right)}$

Calculation for probability lower than average

In an Emotional Health Index score, there are $14$vocations.

Average of EHIS is,

Average $=$$\frac{\mathrm{Total}\mathrm{occupations}}{2}$

$=\frac{14}{2}$

$=7$

The probability is,

$\mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{Average}}{\mathrm{Total}\mathrm{no}\mathrm{of}\mathrm{events}}$

$\mathrm{P}\left(\mathrm{A}\right)=\frac{7}{14}$

$=\frac{1}{2}$