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Probability Distribution and Possible Outcomes

TRUE OR FALSE (With justification)?

If in a probability distribution you got the sum of probabilities less than one, it may mean that you skipped some possible outcome/outcomes.

Health insurance policies are set up in such a way that a healthy person has a negative expected value, and a sickly person has a positive one.

If a distribution curve is bell-shaped, then this is a normal distribution.

If a distribution is normal, its curve is bell-shaped.

A normal distribution curve may be symmetric, left-skewed, or right-skewed.

Because the tails of the normal distribution curve are infinitely long, the total area under the curve is also infinite.

The higher the confidence level, the narrower the confidence interval.

A good way to decrease a confidence interval is to bring down the confidence level.

A good way to decrease a confidence interval is to increase the sample size.

Of these two formulas, 7-2 and 7-3, the first one never results in a greater sample size than the second formula.

A pre-election survey showed that Candidate A got 52%, and Candidate B got 48%. The margin of error is 3%. There is not enough reason for Candidate A to rejoice.

Solution Preview

(1) If in a probability distribution you got the sum of probabilities less than one, it may mean that you skipped some possible outcome/outcomes.

TRUE. If the total probability is less than (or greater than) one, then something went wrong. The total probability should be equal to one.

(2) Health insurance policies are set up in such a way that a healthy person has a negative expected value, and a sickly person has a positive one.

TRUE (from the perspective of the person paying for health insurance). It depends on what perspective you take. It is expected that a healthy person will pay more to the insurance company than they will get from the insurance company. This gives the insurance company a profit when it comes to that person -- that would be a positive expected value for the insurance company. The healthy person would have a negative expected value because they expect to pay ...

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