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?

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

Step-by-step 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

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

tangent

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.