Simple Statistics Review Questions. Please Help

#1
So i have a review test on monday, and i'm trying to get through these review questions. Unfortunately i have no idea how to do some of these problems and none of my notes are helping. These should be fairly simple to any statistics Pros i would assume. Mind you, these are only a few of the many many many review problems all the rest of which ive done on my own and understand. Thank you for any help!

1) The concession manager of a local entertainment venue just had 2 cancellations on his crew. This means that if more than 72,000 people come to tonight’s event, the concession lines will be excessively long, and this will harm business. The manager knows from experience that the number of people who attend this type of event (X) is ~N(67,000, 4,000).

a) What is the probability that there will be more than 72,000 people at the event?
I Think i got Part A. I did (72000-67000)/4000 = 1.25 = Z
1-P(Z<1.25) = .1056 via ZTable


b) Suppose the manager can hire two temporary employees to make sure business won’t be harmed in the future at an additional cost of $200. If he believes the future harm to the business from having more that 72,000 people at the event is quantified at $5000, show that he should hire the employees?
for Part B i have no idea what the question means? isnt it obvious that if it costs him $200 for 2 additional employees, and he thinks having no extra employees is a $5000 potential cost.. Im just not sure what it means.

46. Mr. Bill invests $10,000 in a certain stock on January 1. Having examined past movements of this stock and consulting with his broker, Mr. Bill estimates that the annual return from this stock, X, is Normally distributed with mean 10% and standard deviation 4%. Here X (when expressed as a decimal) is the profit Howard receives per dollar invested. Because Mr. Bill is in the 33% tax bracket, he will then have to pay the Internal Revenue Service 33% of his profit.

a) Calculate the probability that Mr. Bill will have to pay the IRS at least $400.
I tried this one forever.. I kept getting z = 22.5 because i have no idea where to begin or what to do
b) Determine the value for Mr. Bill’s after-tax profit such that he is 90% certain after-tax profit will be less than this amount, i.e., determine the 90th percentile of his after-tax profit.


47. Approximate the following binomial probabilities by the use of normal approximation. Twenty percent of students who finish high school do not go to college. What is the probability that in a sample of 80 high school students
a) exactly 10 will not go to college? I know this is suppost to equal .0274 I have again no idea how to get it, i tried finding variance by 16*(1-.20) = 12.8- and taking the sqrt to get 3.58 then pluging in (10 -16)/3.58 but this is apparently wrong
b) 70 or more will go to college?

c) 14 or fewer will not go to college?

48. Suppose that X is the time (in minutes) required to complete one of two tasks in an assembly process, and Y is the time (in minutes) required to complete the second of two tasks in the assembly process. X and Y are independent. Further, suppose X~N(10, 4) and Y~N(15, 3). Let T = X + Y. What is the probability that it will take more than one-half hour to fully assemble one item?
Ive never seen this type of problem in my notes.. idk where to even begin or what to use.
 

Dason

Ambassador to the humans
#2
b) Suppose the manager can hire two temporary employees to make sure business won’t be harmed in the future at an additional cost of $200. If he believes the future harm to the business from having more that 72,000 people at the event is quantified at $5000, show that he should hire the employees?
for Part B i have no idea what the question means? isnt it obvious that if it costs him $200 for 2 additional employees, and he thinks having no extra employees is a $5000 potential cost.. Im just not sure what it means.
Is it obvious though? If there were only a probability of .0000000000001 that there would be more than 72,000 people do you think it would be justified to spend the extra $200? At that point it would just seem like throwing away the $200. Is there a way for you to figure out how much money the manager can *expect* to lose (at least in terms of costs) in each of the two situations?
 
#3
So basically for your second question, it will cost him $200 to guarantee that there is no future harm to his business.

On the other hand, there is a 10.56% chance that more than 72,000 people will attend (i'm using your numbers, haven't checked them). So there is 10.56% chance that the business will be harmed by $5,000. Thus the Expected Harm for having > 72,000 people is 10.56% * $5,000 or $528 dollars.

Therefore the Expected harm is > the cost of brining new people in, so he bring people in.

For your next question.... It is saying he has to pay uncle same 33% of his profit. So what is the probability he will pay uncle same >=$400.... Answer this first, what profit would you need (minimum) to pay uncle same $400 if you are giving away 33% of your total money...

Now, once you get that, what % return is that amount compared to his original value of $10,000?

Now, what is the probability of getting a % return at least that high from your z scoreS?


For the third question... remember that a Z score for a normal approximation to the Binomial is X (your value) - NP / sqrt(Np*(1-p))... You want the probability of exactly 10 people. That is equal to the probability of 10 or less people minus the probability of 9 or less people.... The other one is simply "probability of less than X people or More than X people"

Remember to use the Continuity Adjustment, and this should be quite simple.

Hope that helps get you started!!