Salaries differ greatly between faculty members at public universities in the united states. full professors (who have tenure and do research) earn an average of $125,572 per year with a standard deviation of $18,328. associate professors (who are working towards tenure and do research) earn an average of $90,101 per year with a standard deviation of $12,741. lecturers (whose primary responsibility is teaching and do not earn tenure) earn an average of $59,707 per year with a standard deviation of $7,386. assume all three populations are normally distributed.
a. what is the probability that a randomly selected full professor makes less than $100,000 per year?

We standardize the $100,000 as a z score of

z = (100,000 - 125572)/18328 = -1.395

That's 1.4 standard deviations below the mean.   We look up the area of the standard normal from -infinity to -1.40 standard deviations and find

P(salary < $100,00) = 0.08076 = 8%

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.