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1. A jar contains 1 red ball, 3 green balls, and 2 yellow balls. Tabulate a sample space for the
following experiments.
a. A single ball is drawn.
b. A ball is drawn and pocketed. A second ball is drawn and pocketed. (You might want to use a
tree diagram).
c. A ball is drawn, its color is recorded, and it is replaced in the jar. A second ball is drawn.
2. Suppose that P(A) = 0.53, P(B) = 0.38, and P(A ∩ B) = 0.21. Compute the following
()
a. P A
b. P ( A B)
c. P(A|B)
3. In a certain town, 39% of the households have a pool, 48% have a vegetable garden, and 67%
have either a pool or a vegetable garden (or both). What is the probability that a randomly selected
household in this town has both a pool and vegetable garden.
4. A single card is drawn from a standard 52-card deck. If A is the event of getting a card that is a
diamond and B is the event getting a face card (jack, queen, or king), calculate the following:
a. P(A)
b. P(A ∩ B)
c. P
(B)
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You work as a business analyst within the IT Department of XYZ Corporation and have just been put on assignment as a consultant to a health care organization. In this organization, there is a clinical “Nurse Helpline” call center, which has a staff of several experienced nurses and nurse practitioners to answer telephone calls from outpatients who have concerns about their health or the treatment or medications they are receiving from the hospital. One of the leading metrics in this call center is hold times. They have a standard that any call placed on hold is not in hold status for more than 2 minutes before an interaction with a nurse. Every day, each clinic records the number of calls and the number of calls on hold answered in less than 2 minutes. The management team has concerns about the number of calls that have hold times greater than 2 minutes. They want to employ a more formal quality control process that would allow them to get ahead of the problem, which is why you have been consulted.
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Provide an example of a control chart (either one you create or one you locate on the web) and label the parts of the chart. (1 slide)
Describe the derivation of the center line and control limits on a control chart and the meaning of each. (1–2 slides)
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Submit your presentation based on the following prompts.
Part 1: Explaining Statistical Process Control (8–10 slides, with speaker’s notes)
Define statistical process control (SPC) and briefly describe the history of SPC, focusing on its origins. (2 slides)
Provide an example of a control chart (either one you create or one you locate on the web) and label the parts of the chart. (1 slide)
Describe the derivation of the center line and control limits on a control chart and the meaning of each. (1–2 slides)
Explain the two types of process variation—common cause and special cause. (2 slides)
Describe at least two signals of special cause variation that might be detected in a control chart. (2–3 slides)
Part 2: Applications of SPC in Business Decision Making (5–8 slides, with speaker’s notes)
Identify at least two examples of the application of SPC in a business context. Select examples from multiple industries (e.g., manufacturing, health care, and service). For each example, describe how SPC was used to improve process, achieve better outcomes, and support sound decision making. (2–4 slides)
For each type of process variation, describe the implications for management action. (2 slides)
In conclusion, provide three potential benefits of SPC to the health care organization. Specifically, how might SPC help the company make sound decisions to the end of achieving its goals? Also, what, if any, drawbacks do you see to using SPC? Identify two possible risks of the use of SPC that the organization should be aware of. (1–2 slides)
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