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## Statistics Exam (Mainly Probability)

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Hello! URGENT EXAM!!!! Statistical exam for social sciences. I would be very happy if someone can help. It would be the best if you can answer all the questions but al least 2 questions are enough. Thanks

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### Additional Instructions

Question 1. (30 points)
We want to get information on working status of younger generation using working status of older generation.
There are three working status high(H), middle(M), and low(L). We denote working status as Ho, Mo, and Lo for older generation and Hy, My, and Ly for younger generation. 10% of older generation works in a high status job, 40% of older generation works in a middle status job, and 50% of older generation works in
a low status job.
The following table shows the transition probabilities. (Hint: transition probabilities show the probability
of working status of younger generation conditional on working status of older generations).
Hy. My. Ly
Ho 0.45 0.48 0.07
Mo 0.05 0.70 0.25
Lo 0.01 0.50 0.49
Answer the following questions based on these information.
a. (5 points) What is the probability of younger generation having a middle status job given the older generation has a higher status job?
b. (10 points) What is the probability of younger generation having a high status job?
c. (15 points) What is the probability of older generation having a high status job given the younger generation is in a higher level job?
Question 2. (30 points)
Average number of patient visits of an emergency room(ER) in an hospital is 5 patients per 30 minutes.
Find the following probabilities.
a. (5 points) What is the probability of no patient visiting the ER within 30 minutes?
b. (5 points) What is the probability of 1 patient visiting the ER within 30 minutes?
c. (10 points) What is the probability of at least 3 patients visiting the ER within 30 minutes?
d. (10 points) What is the probability of 8 patients visiting the ER within an hour?
Question 3. (40 points)
A survey that asks the amount of cash in pocket is conducted on 250 students. The cash amount changes between 0-200 Turkish Lira. The sample has normal distribution with mean 60 lira and standard deviation of 10. Find the following probabilities.
a. (5 points) What is the probability of a student having more than 70 lira?
b. (5 points) What is the probability of a student having less than 40 lira?
c. (10 points) What is the probability of a student having more than 40 and less than 70 lira?
d. (10 points) Suppose the mean of the sample is the same but standard deviation is 20. What is the probability of a student having more than 40 and less than 70 lira?
e. (10 points) Compare your findings in c and d. What happens to the probabilities when the standard deviation increases?

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