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Orders are received for one of four types of parts. The interarrival time between orders is exponentially distributed with a mean of 10 minutes. The table that follows shows the proportion of the parts by type and the time to fill each type of order by the single clerk. Orders of types A and B are picked up immediately after they are filled, but orders of types C and D must wait 10 ± 5 minutes to be picked up. Tabulate the distribution of time to complete delivery for all orders combined. What proportion take less than 15 minutes? What proportion take less than 25 minutes? Simulate for an 8-hour initialization period, followed by a 40-hour run. Do not use any data collected in the 8-hour initialization period.

Orders are received for one of four types of parts. The interarrival time between orders is...

 
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A building-materials firm loads trucks with two pay loader tractors. The distribution of truck-loading times has been found to be exponential with a mean loading_ time of 6 minutes. The truck interarrival time is exponentially distributed with an arrival rate of 16 per hour. The waiting time of a truck and driver is estimated to cost $50 per hour. How much (if any) could the firm save (per 10-hour day) if an overhead hopper system that would fill any truck in a constant time of 2 minutes is installed? (Assume that the present tractors could and would adequately service the conveyors loading the hoppers.)

 

 
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Three independent widget-producing machines all require the same type of vital part, which needs frequent maintenance. To increase production, it is decided to keep two spare parts on hand (for a total of 2 + 3 = 5 parts). After 2 hours of use, the part is removed from the machine and taken to a single technician, who can do the required maintenance in 30 ± 20 minutes. After maintenance, the part is placed in the pool of spare parts, to be put into the first machine that requires it the technician has other duties, namely, repairing other items which have a higher priority and which arrive every 60 ± 20 · minutes requiring 15 ± 15 minutes to repair. Also, the technician takes a 15-minute break in each 2-hour time period. That is, the technician works 1 hour 45 minutes; takes off 15 minutes, works 1 hour 45 minutes, takes off 15 minutes, and so on. (a) What are the model's initial conditions-that is, where are the parts at time O. and what is their condition? Are these conditions typical of “steady state”? (b) Make each replication of this experiment consist of an 8-hour initialization phase followed by a 40-hour data-collection phase. Make four statistically independent replications of -the experiment all in one computer run (i.e.; make four runs with each using a different set of random numbers); (c) Estimate the mean number of busy machines and the proportion of time the technician is busy. (d) Parts are estimated to cost the company $50 per part per 8-hour day (regardless of how much they are in use). The cost of the technician is $20 per hour. A working machine produces widgets worth $100 for each hour of production. Develop an expression to represent total cost per hour which can be attributed to widget production (i.e., not all of the technician's time is due to widget production). Evaluate this expression, given the results of the simulation.

 

 
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Project Goals: The main goal of this project is to help students to build skills in statistical analysis by applying the descriptive statistics tools to estimate the mean COVID-19 Total Cases per 100,000 people (C19TCP100T) and the mean COVID-19 Proportion of Total Deaths in Total Cases (C19PTDITC) for each of your two selected US selected states, and then use those estimates and the inferential statistics to test the difference in COVID-19 incidences across the two selected states. Attached Files: • ECON 351-555 Fall 2021 – Working File – Chapter 3.xlsx (9.468 KB) Students are expected to write their final research report which must describe the population of interest to the analysis, the data collection procedure, the implementation of the statistical procedure to estimate the population parameters (mean C19TCP100T and the mean C19PTDITC) using the sample data, the interpretation of the results, and the policy recommendations. Problem Statement The coronavirus disease 2019 (COVID-19), which appeared first in China in late 2019, has spread quickly across the world, causing in its way significant health, economic, demographic, and social disruptions. What was initially seen as a largely China-centric shock has ballooned to full blown global crisis. On March 11, 2020, the World Health Organization (WHO) declared COVID-19 a global pandemic. COVID-19 has brought forth new challenges such as social distancing, requirement to wear masks in public place, teleworking, prohibition of large-scale social events, travel restrictions and others. Overcoming those challenges has proved to be the best way to contain the spread of the pandemic and protect lives. In the particular case of the United States, each state has set forth strategies to contain the spread of the disease and to reduce the number of deaths. Project Description You are tasked with determine whether or not there exits difference in COVID-19 incidences across two US states of your choice using COVID-19 data, namely, Total Cases and Total Deaths and US population data by state. To complete your project, you will use secondary; 2020 CDC COVID-19 Cases and Deaths by State over time – 2020 (https://data.cdc.gov/Case-Surveillance/United-StatesCOVID-19-Cases-and-Deaths-by-State-o/9mfq-cb36/data ) to estimate the difference in COVID-19 incidences across two states (The Excel file on this dataset is attached). You will also have to test the hypothesis of no difference in COVID-19 incidences across two states. Steps for conducting the statistical analysis are described below. 1. Data collection and visualization – Part 1 (Due Date: 10/01/2021) The dataset on COVID-19 Total Cases and Total Cases by state in 2020 and on the US population by state in 2020 is attached. Select a simple random sample for your selected states which must be the third of the total number of observations. If the third of observations is less than 30, increase the number to 30 by randomly selecting the missing observations. Next, generate the COVID-19 Total Cases per 100,000 people (C19TCP100T) and the COVID-19 Proportion of Total Deaths in Total Cases (C19PTDITC) To generate the C19TCP100T for each state, generate first the population in 100,000 units by dividing the population of state by 100,000. Then, divide Total Cases by the population in 100,000 units to generate the C19TCP100T for each state. To generate C19PTDITC for each state, divide the Total Deaths for the state by the Total Cases for the same state and multiply the results by 100 to express it as a percent. Next, plot the C19TCP100T for the two samples in the same chart (visualization) to detect whether or not there exist differences in Total Cases per 100,000 people. Do the same for the C19PTDITC. The visualizations should be presented using EXCEL.
 
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