Cross Sectoral Response Discussion – Transportation: Early Work HoursTransportation: Early Work HoursBackground: “WHEN POLICY MAKERS talk about solutions to inequality, they usually focus on education and jobs. But this conversation largely ignores the need for improved transportation infrastructure to provide access to these jobs and schools. Through better transportation, American cities can provide opportunities for millions to escape poverty. Yet infrastructure improvement wanes, with Washington unable to do anything despite bipartisan support” (https://www.bostonglobe.com/opinion/2015/05/25/public-transportation-can-ride-out-poverty/KtzBMWFo1Xpsqks7NfbYxL/story.html (Links to an external site.), retrieved 12/15/18).How can public transit help people out of poverty? In communities where there is a lack of adequate bus access and limited taxi/uber/lyft availability due to a spread out metro region, transportation inequality is more pronounced.Instructions:You should include the following in your discussion:PLEASE NOTE: There is no right or wrong answer…the point is to understand that ALL sectors need to be involved if we are going to effectively address issues that impact people in our communities.
Instructions:
There are 4 business situations (55 Points) and 30 Multiple choice questions (45 Points)
Please show all your work in a succinct manner.
If no explanation is provided, the grade would be 50 percent or less in that question.
Business Situation # 1: (20 Points) The Fire Department records how long it takes each of its trucks to reach the scene of a fire. The distribution of the arrival times is uniform with the minimum time being 2 minutes and the maximum time 15 minutes.
Draw the uniform probability distribution diagram.
What is the probability that a truck will reach a fire scene within 5 to 10 minutes?
What is the expected time (mean time) until arrival?
What is the standard deviation of truck arrival times?
Business Situation # 2: (10 points) Seven sprinters have advanced to the final heat at a track meet.
How many ways can they finish?
How many ways can they finish in first, second and third place.
Business Situation # 3: (10 points) In South Carolina’s Carolina 5 lottery, a player selects five different numbers from 1 to 36 (Inclusive). If the numbers selected match the players numbers in any order, the player wins.
Business Situation # 4: (15 points) The service manager for United Airlines is uncertain about the time needed for the ground crew to turn an airplane around from the time it lands until it is ready to takeoff. He has been told that the times seems to range between 15 to 45 minutes.
Apply a uniform distribution to the turnaround.
Compute the mean
Compute the standard deviation.
Please select the appropriate option and explain why you did so.
1) If the variance is 81 grams, what is the standard deviation four times?
A) 0.600
B) 1.897
C) 6.000
D) 36.00
2) A total of 60% of the customers of a fast-food chain order a hamburger, French fries, and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?
A) 0.186
B) 0.403
C) 0.000
D) 1.000
3) Judging from recent experience, 15% of the computer keyboards produced by an automatic, high-speed machine are defective. If six keyboards are randomly selected, what is the probability that none of the keyboards are defective?
A) 0.001
B) 0.167
C) 0.735
D) 0.500
4) On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?
A) 0.002
B) 0.344
C) 0.599
D) 0.100
5) A listing of all possible outcomes of an experiment and their corresponding probabilities of occurrence is called a ________.
A) random variable
B) probability distribution
C) subjective probability
D) frequency distribution
6) Which one of the following is a condition of the binomial distribution?
A) Non-Independent trials
B) Only two outcomes
C) The probability of success changes from trial to trial
D) Sampling at least 10 trials
7) Which is true for a binomial distribution?
A) There are 10 or more possible outcomes.
B) The probability of success remains the same from trial to trial.
C) The value of π is equal to 1.50.
D) It approximates the Poisson distribution.
8) Sponsors of a local charity decided to attract wealthy patrons to its $500-a-plate dinner by allowing each patron to buy a set of 20 tickets for the gaming tables. The chance of winning a prize for each of the 20 plays is 50–50. If you bought 20 tickets, what is the chance of winning 15 or more prizes?
A) 0.250
B) 0.021
C) 0.006
D) 0.750
9) What kind of distributions are the binomial and Poisson probability distributions?
A) Discrete
B) Continuous
C) Both discrete and continuous
D) Neither discrete nor continuous
10) Which of the following is not correct about a probability distribution?
A) The sum of all possible outcomes must not equal 1.0.
B) The outcomes must be mutually exclusive.
C) The probability of each outcome must be between 0.0 and 1.0 inclusive.
D) All of these answers are correct.
11) Data show that the weight of an offensive linesman may be any weight between 200 and 350 pounds. The distribution of weight is based on a ________.
A) Continuous random variable
B) Discrete random variable
C) Qualitative variable
D) All of these answers are correct.
12) Carlson Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks of the purchase date. Their records reveal that 10% of the diamond wedding rings are returned. Five different customers buy a wedding ring. What is the probability that none of the customers return a ring?
A) 0.250
B) 0.073
C) 0.590
D) 0.500
13) In a large metropolitan area, past records revealed that 30% of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?
A) 0.114
B) 0.887
C) 0.400
D) 0.231
14) Chances are 50–50 that a newborn baby will be a girl. For families with five children, what is the probability that all the children are girls?
A) 0.900
B) 0.031
C) 0.001
D) 0.250
15) A manufacturer of headache medicine claims it is 70% effective within a few minutes. That is, out of every 100 users, 70 get relief within a few minutes. A group of 12 patients are given the medicine. If the claim is true, what is the probability that eight have relief within a few minutes?
A) 0.001
B) 0.168
C) 0.667
D) 0.231
16) A true/false test consists of six questions. If you guess the answer to each question, what is the probability of getting all six questions correct?
A) 0
B) 0.016
C) 0.062
D) 0.250
17) A tennis match requires that a player win three of five sets to win the match. If a player wins the first two sets, what is the probability that the player wins the match, assuming that each player is equally likely to win each set?
A) 0.500
B) 0.125
C) 0.875
D) 0.000
18) Which of the following is a characteristic of a binomial probability distribution?
A) Each outcome is not mutually exclusive.
B) Each trial is not independent.
C) The probability of success remains changes from trial to trial.
D) The number of trials is unlimited.
19) What must you know to develop a binomial probability distribution?
A) The probability of success
B) The probability of success and the number of trials
C) The probability of success and the number of successes
D) The number of trials and the number of successes
20) David’s gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that at least 10 pay in cash?
A) 0.024
B) 0.033
C) 0.009
D) 0.976
21) David’s gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that all 15 pay in cash?
A) 0.0
B) 0.1
C) 0.9
D) 1.0
22) David’s gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. This situation is an example of what type of discrete probability distribution.
A) Continuous probability distribution
B) Poisson probability distribution
C) Binomial probability distribution
D) Hypergeometric probability distribution
23) A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.
Number of Days Absent
Probability
0
0.60
1
0.20
2
0.12
3
0.04
4
0.04
5
0.00
What is the variance of the number of days absent?
A) 1.1616
B) 1.41
C) 5.00
D) 55.52
24) For the following distribution:
x
P(x)
0
0.130
1
0.346
2
0.346
3
0.154
4
0.026
What is the mean of the distribution?
A) 1
B) 2.5
C) 1.604
D) 3
25) For the following distribution:
x
P(x)
0
0.130
1
0.346
2
0.346
3
0.154
4
0.026
What is the variance of the distribution?
A) 1.1616
B) 0.964
C) 0.982
D) 1.000
26) For the following distribution:
x
P(x)
0
0.027
1
0.189
2
0.441
3
0.343
What is the mean of the distribution?
A) 2.1
B) 1.5
C) 0.441
D) 2
27) For the following distribution:
x
P(x)
0
0.027
1
0.189
2
0.441
3
0.343
What is the variance of the distribution?
A) 2.1
B) 0.63
C) 3.9
D) 2.754
28) For a binomial distribution, the mean is 0.6 and n = 6. What is π for this distribution?
A) 0.5
B) 1.00
C) 0.3
D) 0.1
29) For a binomial distribution, the mean is 24.0 and n = 8. What is π for this distribution?
A) 0.5
B) 1.00
C) 3.0
D) 0.1
30) In which of the following discrete distributions does the probability of a success vary from one trial to the next?
A) Binomial
B) Poisson
C) Hypergeometric
D) All of these answers are correct.
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