AssignmentAnswer all the questions.1. If Project A has the following probability distribution of forecast profits:Prob : XXXXXXXXXXProfit/ Loss : XXXXXXXXXXShould he invest in project A or not? Why?2....

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Assignment



Answer all the questions.



1. If Project A has the following probability distribution of forecast profits:



Prob : 0.1 0.3 0.4 0.2



Profit/ Loss : -800 -200 400 500



Should he invest in project A or not? Why?



2. Assuming that the customer arrivals at the Fidelity Credit Union drive through window are Poisson distributed with a mean of five per hour , find



a. The probability that in a given hour more than eight customers will arrive at the drive-through window.



b. The probability that between three and six customers inclusive, will arrive at the drive through window in a given hour.



c. The probability that fewer than three customers will arrive at the window in a given 30 minute period.



3. A small southern West Australian country town has maintained records showing that the daily maximum temperature during summer (Dec.,Jan.,Feb.) has averaged 30 degree Celsius with a standard deviation of 5 degree Celsius. Further, the maximum temperature appears to be approximately normally distributed.



Find:



(a) the percentage of summer days that will have a maximum temperature between 30C & 35C.



(b) the percentage of days that the maximum temperature will exceed 37.5 C



(c) the probability that the maximum temperature will be less than 24 C.



(d) the proportion of summer days that the maximum temperature will be between 18C and 20C



(e) The maximum temperature that will be exceeded only 5% of the time.



4. Explain the different types of probability and non-probability sampling techniques.



5. The general manager of Western Software Pty Ltd believes that 30% of the firm’s orders come from new or first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of new or first-time customers. The results of the sample will be used to verify the general manager’s claim of p = 0. 30.



(a) Assume that the general manager is correct and p = 0.30, what is the sampling distribution of p for this study.



(b) What is the probability that the sample proportion p will be between 0.2 and 0.4?



(c) What is the probability that the sample proportion will be within plus or minus 0.05 of the population proportion p = 0.30?
Answered 2 days AfterDec 20, 2022

Answer To: AssignmentAnswer all the questions.1. If Project A has the following probability distribution of...

Parvesh answered on Dec 22 2022
31 Votes
1) Expected value of profit is given by

He should invest in project A. Because , expected value of profit is positive. It means
he will get profit by investing in project A.
                ......................................
2) Here,
Formula used:     
a) Here, we have to find P(x>8)

b) Here, we have to find
c) Here,
Here, we have to find P(x<3)
                ..........................................
3) Here,
a) Here, we have to find P(30
b) Here, we have to find P(x>37.5)

c) Here, we have to find P(x>24)
d) Here, we have to find P(18e) We have to find x such that P(z>c)=0.05 or P(z=>c= 1.645 (using =NORMSINV(0.95) in excel. )
Now,
Maximum temperature= 38.23 C
                ....................................
4)
Probability sampling techniques:
Simple random sampling
Simple random sampling gathers a random selection from the entire population, where each unit has an equal chance of selection.
Stratified sampling
Stratified sampling collects a random selection of a sample from within certain strata, or subgroups within the population. Each subgroup is separated from the others on the basis of a common characteristic, such as gender, race, or religion.
Systematic sampling
Systematic sampling draws a random sample from the target population by selecting units at...
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