What is the standard deviation of individual bags if sample averages are based on 5 bags? Explain your finding. Hint: x-bar = /sqrt(n). Having x-bar based on part a calculation, solve for  given n= 5.

On November 1, 2013 John Adams, a customer service representative of Americo Drilling Supplies (ADS), was summoned to the Houston office of Drilling Contractors, Inc. (DCI), to inspect three boxcars of mud-treating agents that ADS had shipped to the Houston firm. DCI had filed a complaint that the 25 Pound bags of treating agents that it had just received from ADS were short-weight by approximately at least 2%.
The light-weight bags were initially detected by one of DCI’s receiving clerks, who noticed that the rail road side scale tickets indicated that the net weights were significantly less on all three of the boxcars than those of identical shipments received on October 25, 2013. ADS’s traffic department was called to determine if lighter-weight dunnage or pallets were used on the shipments. (This might explain the lighter weights.) ADS indicated, however, that no changes had been made in the loading or palletizing procedures. Hence, DCI randomly checked 25 of the bags and discovered that the average net weight was 24.5 pounds. Consequently, they concluded that the sample indicated a significance short-weight. ADS, was then contacted, and Adams was sent to investigate the complaint and to issue credit (???) to DCI.
DCI, however, was not completely satisfied with only the issuance of credit for the short shipment. The charts followed by their mud engineers on the drilling platforms were based on 25-pound bags of treating agents. Lighter-weight bags might result in poor chemical control during the drilling operation and might adversely affect drilling efficiency. (Mud-treating agents are used to control the pH and other chemical properties of the open during drilling operations.) This could cause severe economic consequences because of the extremely high cost of oil and natural gas drilling operations. Consequently, special use instructions had to accompany the delivery of these shipments to the drilling platforms. Moreover, the light-weight shipments had to be isolated in DCI warehouse, causing extra handling and poor space utilization. Hence, Adams was informed that CDI might seek a new supplier of mud-treating agents if in the future it received bags that deviated significantly below 25 pounds.
The quality control department at ADS suspected that the light-weight bags may have resulted from “growing pains” at the Orange, Texas plant. Because of the earlier energy crises, oil and natural gas exploration activity had greatly increased. This increased activity, in turn, created increased demand for products produced by related industries, including drilling muds. Consequently, ADS had to expand from one shift (6 A.M. to 2 P.M.) to a two-shift (2 P.M. to 10 P.M.) operation in Mid 2011s, and finally to a three-shift operation (24 hours per day) in January of 2013.
The additional night shift bagging crew was staffed entirely by new employees. The most experienced foremen were temporarily assigned to supervise the night shift. Most emphasis was placed on increasing the output of bags to meet the ever-increasing demand. It was suspected that only occasional reminders were made to double-check the bag weight feeder. (A double check is performed by systematically weighting a bag on a scale to determine if the proper weight is being loaded by the weight-feeder. If there is significant deviation from 25 pounds, corrective adjustments are made to the weight-release mechanism.)
To verify this expectation, the quantity control staff at ADS randomly sampled the bag output and prepared the following table (see Excel dataset). Five bags were sampled and weighted each hour.
Assume you are John Adams of ADS. Based on the following analysis, prepare a report to be submitted to both ADS and DCI executives regarding the status of the filling process at ADS and recommend method to improve quality control at the filling station and estimate the amount of credit to DCI. Use the data provided in the Excel data file.
Insert all graphs and provide analysis in this word file after every question. Only The Word file is graded.
a- Calculate the Range Column in Excel (Largest-Smallest) and find mean and standard deviations for Average Weight, Smallest, Largest, and Range columns.
b- What is the standard deviation of individual bags if sample averages are based on 5 bags? Explain your finding. Hint: x-bar = /sqrt(n). Having x-bar based on part a calculation, solve for  given n= 5.
c- Construct a time series plot of all four variables (two graphs: one includes avg., smallest, and largest and the other has range) and discuss your findings based on the graphs.
d- Construct X-bar and R Charts, graph, and discuss your findings based on the control charts. Is the process out of control? Why? Explain.
e- Is there any differences between performances of three shifts? Hint: (Carve out the morning, afternoon, and night shift data into three columns and graph their averages. Explain your findings based on

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