Completing the spreadsheet, all the tabs need to be completed.
Dis. Prob. Dist -
Q1. For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months. Suppose the following data are for particular region in upstate New York. The values in the first columns show the corresponding number of unemployed persons
|
Months Unemployed
|
P(x)
|
X*P(x)
|
X-Expected Value
|
(X-Expected Value)^2
|
(X-Expected Value)^2*P(x)
|
|
1
|
0.038
|
0.038
|
-4.82
|
23.27
|
0.89
|
|
2
|
0.063
|
0.125
|
-3.82
|
14.62
|
0.91
|
|
3
|
0.084
|
0.252
|
-2.82
|
7.97
|
0.67
|
|
4
|
0.099
|
0.397
|
-1.82
|
3.33
|
0.33
|
|
5
|
0.129
|
0.646
|
-0.82
|
0.68
|
0.09
|
|
6
|
0.172
|
1.035
|
0.18
|
0.03
|
0.01
|
|
7
|
0.154
|
1.076
|
1.18
|
1.38
|
0.21
|
|
8
|
0.133
|
1.064
|
2.18
|
4.74
|
0.63
|
|
9
|
0.086
|
0.776
|
3.18
|
10.09
|
0.87
|
|
10
|
0.042
|
0.415
|
4.18
|
17.44
|
0.72
|
|
Expected Value - 5.82
|
|
Variance - 5.3
|
|
|
|
|
Standard Deviation -
2.31
|
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x
b. What is the probability that a person is unemployed for two months or less? Unemployed for months than two months?
c. What is the probability that a person is unemployed for more than six months?
Q2. The demand for a product of California Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company's monthly demand.
|
Unit Demand
|
Probability
|
X*P(x)
|
X-Expected Value
|
(X-Expected Value)^2
|
(X-Expected Value)^2*P(x)
|
|
300
|
0.2
|
|
|
|
|
|
400
|
0.3
|
|
|
|
|
|
500
|
0.35
|
|
|
|
|
|
600
|
0.15
|
|
|
|
|
|
Expected Value
|
|
|
Variance
|
|
|
|
|
|
Standard Deviation
|
|
a. If the company bases monthly orders on the expected value of the monthly demand, what should Carolina's monthly order quality be for this product?
b. Assume that each unit demanded generates $70 in revenue and each unit ordered cost $50. How much will the company gain or lose in a month if it places an order based on your answer to part (1) and the actual demand for the item is 300 units?
Binomial:
Q1. When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number defective parts found.
a. Describe the conditions under which this situation would be a binominal experiment
b. Draw a tree diagram showing this problem as a two-trial experiment.
c. How many experimental outcomes result in exactly one defect being found?
d. Compute the probabilities associated with finding no defects exactly one defect, and two defects.
Q2. Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliable question is whether a detection system will be able to identify and attack and issue a warning. Assume that a particular detection system has a 0.90 probability of detecting a missile attack. Use a binominal probability distribution to answer the following questions.
a. What is the probability that a single detection system will detect an attack?
b. If two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack?
c. If three systems are installed, what is the probability that at least one of the systems will detect the attack?
d. Would you recommend that multiple detection system is used? Explain.
Q3. A university found that 20% of their student withdraws without completing the introductory statistics course. Assume that 20 students registered for the course.
a. Compute the probability that 2 or fewer will withdraw
b. Compute the probability that exactly 4 will withdraw
c. Compute the probability that more than 3 will withdraw
d. Compute the expected number of withdrawals.
Poisson:
Q1. Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
a. Compute the probability of receiving four calls in a 5-minute interval of time.
b. Compute the probability of receiving exactly 10 calls in 15 minutes.
c. Suppose, no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time? What is the probability that none will be waiting?
d. If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?
Q2. During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.
What is the expected number of calls in one hour?
What is the probability of three calls in five minutes?
What is the probability of no calls in a five-minute period?
Q3. Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 7 passengers per minute.
a. Compute the probability of no arrivals in a one-minute period?
b. Compute the probability that 3 or fewer passengers arrive in a one-minute period?
c. Compute the probability of no arrivals in a 15 second period?
d. Compute the probability of at least one arrival in a 15-second period?
Normal Distribution:
Q1. For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015. Assume the standard deviation is $3540 and that debt amounts are normally distributed
a. What is the probability that the debt for a borrower with good credit is more than $18,000?
b. What is the probability that the debt for a borrower with good credit is less than $10,000?
c. What is the probability that the debt for a borrower with good credit is between $12,000 and $18,000?
d. What is the probability that the debt for a borrower with good credit is no more than $14,000?
Q2. The average return for large-cap domestic stock funds over the three years 2009-2011 was 14.4%. Assume that three-year returns were normally distributed across funds with an standard deviation of 4.4%
a. What is the probability that an individual large-cap domestic stock fund had a three-year return of at least 20%?
b. What is the probability that an individual large-cap domestic stock fund had a three-year return of 10% or less?
c. How big the return have to be to put a domestic stock fund in the top 10%percent of the three-year period?
Q3. The average price for gallon in the United States is $3.73 and in the Russia is $3.40. Assume there averages are the population means in the two countries and that the probability distributions are normally distributed with an standard deviation of $.25 in the United States and a standard deviation of $.20 in Russia.
a. What is the probability that randomly selected gas stations in the United States charges less than $3.50 per gallon?
b. What percentage of the gas station in Russia charge less than $3.50 per gallon?
c. What is the probability that a randomly selected gas station in Russia charged more than the mean price of the United States?
Q4. Television viewing reached a new high when the Nielsen Company reported a mean daily viewing time of 8.35 hours per household. Use a normal probability distribution with standard deviation of 2.5 hours to answer the following:
a. What is the probability that a household views television between 5 and 10 hour a day?
b. How many hours of television viewing ust a household have in order to be in the top 3% of all television viewing households?
c. What is the probability that a household views television more than 3 hours a day?
Income:
The Following crosstabulation shows household income by educational level of the head of household (Statistical Abstract of the United States, 2008)
|
Household Income
|
|
Educational Level
|
Under 25
|
25.0-49.9
|
50.0-74.5
|
75.0-99.9
|
100 or more
|
Total
|
|
Not H.S. Graduate
|
4207
|
3459
|
1389
|
539
|
367
|
9961
|
|
H.S. Graduate
|
4917
|
6850
|
5027
|
2637
|
2668
|
22099
|
|
Some College
|
2807
|
5258
|
4678
|
3250
|
4074
|
20067
|
|
Bachelor's Degree
|
885
|
2094
|
2848
|
2581
|
5379
|
13787
|
|
Beyond Bach. Deg.
|
290
|
829
|
1274
|
1241
|
4188
|
7822
|
|
Total
|
13106
|
18490
|
15216
|
10248
|
16676
|
73736
|
1. Develop a joint probability table.
|
Joint Probability Household Income
|
|
Educational Level
|
Under 25
|
25.0-49.9
|
50.0-74.5
|
75.0-99.9
|
100 or more
|
Total
|
|
Not H.S. Graduate
|
0.06
|
0.05
|
0.02
|
0.01
|
0.00
|
0.14
|
|
H.S. Graduate
|
0.07
|
0.09
|
0.07
|
0.04
|
0.04
|
0.30
|
|
Some College
|
0.04
|
0.07
|
0.06
|
0.04
|
0.06
|
0.27
|
|
Bachelor's Degree
|
0.01
|
0.03
|
0.04
|
0.04
|
0.07
|
0.19
|
|
Beyond Bach. Deg.
|
0.00
|
0.01
|
0.02
|
0.02
|
0.06
|
0.11
|
|
Total
|
0.18
|
0.25
|
0.21
|
0.14
|
0.23
|
1
|
2. What is the probability of a head of household not being a high school graduate?
3. What is the probability of a head household having a bachelor's degree or more education?
4. What is the probability of a household headed by someone having bachelors degree earnings $100,000 or more?
5. What is the probability of a household having income below $25,000
6. What is the probability of a household headed by someone with bachelor's degree earnings less than $25,000?
Attachment:- Assignment Files.rar