Question

ores on the MCAT are normally distributed. If your score is two standard deviations below the mean then you are automatically rejected from residency. If your score is two standard deviations above the mean then you are automatically accepted into residency. The chance of someone being automatically rejected is 0.022. What is the probability that a random student is not automatically rejected or accepted?

Answer 1

There is a 95.6% probability that a random student is not automatically rejected or accepted.

Explanation:

If your score is two standard deviations below the mean then you are automatically rejected from residency. The chance of someone being automatically rejected is 0.022.

If your score is two standard deviations above the mean then you are automatically accepted into residency. In normally distributed samples, the probability of being two standard deviations above the mean is the same of being two standard deviations below the mean, so this is also 0.022.

What is the probability that a random student is not automatically rejected or accepted?

The chance of someone being automatically rejected is 0.022.

The chance of someone being automatically accepted is 0.022.

The sum of the probabilities is decimal 1.

So

`P + 2*0.022 = 1`

`P = 0.956`

There is a 95.6% probability that a random student is not automatically rejected or accepted.