worried about customer complaints and potential lawsuits, the manufacterers decided that no more than o.5% of bags of Crunchy corn chips should be underweight. there are 2 possible adjustments that can be made; change the mean setting on the filling machines while leaving the standard deviation constant, or leave the mean setting at 10.4 ounces and try to adjust the standard deviation. Describe the necessary adjestments for each of these plans. Which do you think is the most feasible? Explain.

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The manufacturers have also discovered that if they put too many chips in a bag the bag will busr. In order to balance their concerns over customer satisfaction and possible breakage, management wants to adjust the filling machines so that only 0.5% bags are under weight and only 2% are mroe than 10.5 ounces. Find the values of Mean and standard deviation that accomplist these goals.

First, you have not provided a ounces cutoff value for "underweight".

Second, take a shot -- what do you think.
Hint -- think normal distribution and look a the number of standard deviations away from the mean that coincides with .5%

A pizza parlor has a choice of toppings for its pizzas. From these toppings, how many different -topping pizzas can be ordered? Assume that the order in which the toppings are listed does not matter.

For the first question, let's analyze the two possible adjustments separately:

1. Adjusting the mean setting on the filling machines while leaving the standard deviation constant:
To ensure no more than 0.5% of bags are underweight, the manufacturers would need to decrease the mean weight of the bags. The necessary adjustment would be to reduce the mean weight to a point where only 0.5% of the bags fall below the required weight. This adjustment aims to decrease the number of underweight bags but does not address the issue of bags being overweight.

2. Leaving the mean setting at 10.4 ounces and trying to adjust the standard deviation:
To achieve the desired outcome of no more than 0.5% underweight bags, the manufacturers would need to decrease the variability in weight by adjusting the standard deviation. This adjustment aims to reduce both underweight and overweight bags, as it affects the spread of weights rather than the center (mean) of the distribution.

Based on feasibility, adjusting the standard deviation seems to be the more realistic option. Changing the mean setting on the filling machines might have unintended consequences, such as increasing the number of overweight bags. By keeping the mean setting constant and focusing on reducing the variability through adjusting the standard deviation, the manufacturers can better control the weights of the bags and minimize the likelihood of both underweight and overweight bags.

Moving on to the second question:

To adjust the filling machines in order to achieve the desired outcomes of having only 0.5% of bags underweight and 2% of bags overweight, we need to find the appropriate mean and standard deviation values.

Let's assume a normal distribution for the weights of the bags. To calculate the mean and standard deviation, we can use the properties of the normal distribution.

1. For the underweight bags:
We want only 0.5% of bags to be underweight, which corresponds to the area to the left of the weight value we are interested in. This area is represented by the z-score. By looking up the z-score in the standard normal distribution table, we find that z = -2.57 for a 0.5% left-tail probability.

Using the z-score formula: z = (X - mean) / standard deviation,
we can rearrange it to get: X = z * standard deviation + mean.

Plugging in the values, we have:
10.4 - 2.57 * standard deviation = desired minimum weight.

2. For the overweight bags:
We want only 2% of bags to be overweight, which corresponds to the area to the right of the weight value we are interested in. This area is also represented by a z-score. From the standard normal distribution table, we find that z = 2.05 for a 2% right-tail probability.

Using the same formula as above, we have:
10.4 + 2.05 * standard deviation = desired maximum weight.

By solving the two equations simultaneously, we can find the values of the mean and standard deviation that accomplish these goals.

However, the exact values cannot be determined without additional information for the standard deviation.

1. Adjustments for the first plan:

- Change the mean setting on the filling machines while leaving the standard deviation constant: To ensure that no more than 0.5% of bags of Crunchy corn chips are underweight, the manufacturers need to adjust the mean filling weight. They can increase the mean filling weight to reduce the likelihood of underweight bags. By increasing the mean, the average weight of the bags will be higher, resulting in fewer bags falling below the desired weight threshold.

2. Adjustments for the second plan:
- Leave the mean setting at 10.4 ounces and try to adjust the standard deviation: In this case, the manufacturers keep the mean setting constant at 10.4 ounces but adjust the standard deviation to meet the requirement of no more than 0.5% underweight bags. Reducing the standard deviation will result in a narrower range of weight distribution, meaning there will be fewer bags that fall below the desired weight threshold.

Feasibility:
While both plans can be used to achieve the desired outcome, adjusting the mean setting on the filling machines is typically easier and more feasible for manufacturers. Changing the mean setting is a controlled adjustment that directly affects the average weight of the bags. The manufacturers can easily calibrate the machines to produce bags with higher average weights, which will result in fewer underweight bags.

On the other hand, adjusting the standard deviation might be more challenging and less practical. It is difficult to control the randomness and variability of the weight distribution by solely changing the standard deviation. Additionally, extensive testing and calibration might be required to achieve the desired outcome. Therefore, adjusting the mean setting is generally considered the most feasible option in this scenario.

For the second part of your question regarding balancing concerns over customer satisfaction and breakage, the values of mean and standard deviation needed to accomplish the goals can be calculated by statistical analysis techniques such as using normal distribution tables or software. The specific values will depend on the desired confidence level and the characteristics of the weight distribution.