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Answer :
Tom needs to use an x-bar chart and an R-chart to analyze the problem of bags not appearing full.
a) The x-bar chart will help him monitor the average weight of the gum drops in each bag, ensuring they meet the 16-ounce requirement. The R-chart will help him monitor the range of weights within each sample, providing insight into the variability of the weights.
b) Tom will need to gather random samples of 10 bags throughout the day and weigh the gum drops in each bag.
c) To construct the x-bar chart, Tom will calculate the average weight of the gum drops in each sample. He will then plot these averages on the chart and calculate the control limits based on the sample size.
To construct the R-chart, he will calculate the range of weights within each sample and plot them on the chart, also calculating the control limits.
d) After completing the charts, Tom should monitor the process over the next week or so, looking for any patterns or trends that indicate issues with the weight of the gum drops.
Tom should use a p-chart to analyze the problem of "too many green ones" in the bags.
a) The p-chart will help him monitor the proportion of green gum drops in each bag, ensuring they are within the acceptable range of 2-4 green ones per bag.
b) Tom will need to gather random samples of 10 bags throughout the day and count the number of green gum drops in each bag.
c) To construct the p-chart, Tom will calculate the proportion of green gum drops in each sample. He will then calculate the overall proportion of green gum drops and the control limits based on the sample size.
d) After completing the chart, Tom should monitor the process over the next week or so, looking for any points outside the control limits or trends that indicate issues with the proportion of green gum drops. He should also investigate any "bad" or "defective" bags with less than 2 or more than 4 green gum drops.
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