James earns $418 per week and has one exemption. His office’s payroll software is broken and can only compute the withholding fo
1 answer:
James should earn a <em>weekly</em> salary of $ 432.76 with 0 exemptions to give the closest exemption.
<h3>How to estimate the salary without exemption</h3>
In this question, we should estimate the salary <em>earned</em> before one exemption and find the <em>equivalent brute</em> salary with no exemptions. The expected salary is equal to product the <em>brute</em> salary minus the product of the <em>tax</em> rate and <em>brute</em> salary.
According to the table we have the expected salary after one exemption:
After a quick inspection to the <em>salary</em> column for zero exemptions, we find that percentage associated to a salary with no exemptions: ()
James should earn a <em>weekly</em> salary of $ 432.76 with 0 exemptions to give the closest exemption.
The exemption table is missing. The complete figure is shown below.
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Your answer is 36%. See work
Answer: a) P = 0.5, b) P = 0.07
Step-by-step explanation:
Hi!
Lets call X₁ the time at which you arrive, and X₂ the time at which Bob arrives. Both are random variables with uniform density in the interval [0, 60] (in minutes). Their joint distribuition is uniform over the square in the image, with value P = 1/(60*60) = 1/3600.
a) For you to get more cake than Bob, you should arrive earlier. This event is A = { X₁ < X₂ }, the shaded triangle in the figure.The area of this event (set) is half the total area of the square, so P(A) = 0.5.
It makes sense, beacuse its equally probable for you or Bob to arrive earlier, as both have uniform density over the time interval.
b) In this case you arrive later than Bob, but less than 5 minutes later. So the event is B = { X₂ < X₁ < (X₂ + 5) } . This is the gray shaded area in b) part of the image. Its area is the difference two triangles (half square - blue triangle), then the probability is:
