PS 2

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School

University of Hawaii *

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310

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Statistics

Date

May 7, 2024

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pdf

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Uploaded by AmbassadorSummerGuineaPig37 on coursehero.com

PROBLEM SET 2 SPRING 2024 Find your problem set via Laulima-> Assignments. Work in a group of at least three. LIST ALL YOUR GROUP MEMBERS, FIRST AND LAST NAME, FOR FULL CREDIT. Type and label questions with the answers into a Word document and copy and 'Paste special', any graphs or tables you have generated in Excel. Do not submit your Excel file! Each member must upload a PDF FORMAT version to the Assignment Folder / PS 2. Thank you! Chapter 4 - Probability: (These problems are like the problems in Sections 4.1 and 4.2). . You may use the two-way table to answer the following questions. (3 points). You need to show your calculations to receive full credit. The table below shows the results of a 2022 study by Boeing and Airbus of parts that failed. The study looked at failed parts that were manufactured in house and subcontracted. They were looking for a difference in manufacturing locations. You want to figure out the probabilities for the following situations. Be sure to show or explain any calculations you make, do not just put down numbers! Auto pilot Electrica l Engine Total Sub-Contracted 12 8 6 26 In House Manufactured 10 15 9 34 Total 22 23 15 60 1. What is the probability that an auto pilot failed? The auto pilot failed 22/60 which = 0.37 to 37.7% 2. What is the probability a subcontracted engine will fail? The probability a subcontracted engine will fail is 6/60 which = 0.1 => 10% 3. What is the probability that an engine will fail given it was produced by a subcontractor? For this is 6/26 = 0.2307 to 23.07%

4. What is the probability an engine built in house will fail? The probability an engine built in house will fail is 9/15 = 0.6 => 60% 5. What is the probability that a plane will have an engine or autopilot failure? = 37/ 60 = 0.6166 = 61.66% 6. Is engine failure dependent upon being built in house or by a subcontractor? Explain logically why and what calculations would provide evidence of this. (Ex 4.8-Table 4.3, page 189 text) Independent (if the ratios are equals then they are independent) 15/60 = .25 to 25% (engine failure to total) 6/26 = 23.07% 9/34 = 26.47% Chapter 6: Normal Probability (These problems are like the problems in Section 6.2). Using a Normal Distribution to find probabilities: Use the table E.2 in your text. Draw a sketch and indicate what probabilities (E.g. P (X<3 and X>10) for what is required for each part of the problem. To make sketches copy and paste into Word for the areas under the bell-curve you have the NormalSketch.ppt PowerPoint slide in the Resources Handout area on Laulima, The main point of providing a sketch is to give you a visual idea of what your solution will be. 1. Do problem ( 5 points) Remember, you need to include completed sketches to receive full credit. You order and manage the medications in the Pharmacy for Queens hospital. The CEO is concerned because the hospital is ordering and stocking medicine with short shelf lives and it’s not being used and thrown away. There is a medicine called Harvoni that is used for Hepatitis. The cost of a treatment is $95,000 and the shelf life for the medicine is 12 weeks. Last year’s significant amount of this medicine was disposed of because of the short shelf life: How many treatments should you order? For this question the mean ( μ) was 20, the standard deviation ( σ ) was 5, skewness was .06 and kurtosis was - .27. a. You can find the probabilities for this problem assuming a normal (bell-shaped) curve. Why is it OK for this particular situation?

Yes it is okay because the skewness and kurtosis is being -1 and 1 which is normal b. What is the probability that you will use no more than10 treatments in a given week? Use the Z-score then use the probability chart . The answer is 2.75% (10-20/5) = -2 c. What is the probability that it will use more than 36 treatments in a given week? Same thing: Use Z score and then so you have to get the minus the probability with 100% because it only goes to the right to left ( This is the rule: it’s a outlier if its 3± SD for getting Z score) It originally get 99.9 (because probability gives you right to left) so minus 100 with 99.9 gives you .1% d. Would using more than 36 treatments in a week be an outlier for this data set? Yes this is an outlier because it is 3.2 which is over the 3±SD Another way is when you do 3 deviation away from the average (20 + (3*5) = 35) but its 36 so yes it’s an outlier e. You expect to use μ number of treatments each day. Because of the variability you will actually sell more or less each day. To understand this, find out how many less or more than μ you expect to sell 80% of the time. That is, find two values equal distance from the mean such that 80% of all values fall between them. Specifically find what number of x treatments where 80% of the values fall between μ - x and μ + x This question is asking 80% this is how much people we treat in-between points The Z-score for 10% is -1.28 and the score for 90% is 1.28 Closest probability to 80% is 0.7995 (1.28 * 5) + 20 = 26.4; (-1.28 * 5) + 20 = 13.6 f. You can only have a fixed amount of treatments on hand to sell every week. As in (e) you know you will surely use more or less than μ treatments each week. If you run out of treatments, your patients will die. But if you order too many treatments, they will go bad and you will have to throw them out, so you are willing to sell out occasionally. How many treatments must you have on hand to sell if you wanted to ensure you do not run out more than 5% of the time? (This is called having a 95% service level) You work backwards again like problem E from probability to Z score to Location. Z score is 1.64 from 95% Multiply the Z-score by the STD f demand to find the safety stock, then add it to the average demand 1.64 * 5 = 8.2 + 20 = 28.2

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