# Question & Answer: Research & Design (R&D) has determined the following: The weight of the overshoes…..

Research & Design (R&D) has determined the following: The weight of the overshoes must be at least 60% of the weight of the “client” in freshwater applications. For example, if the client weighs 100 pounds, the overshoes must weigh at least 60 pounds to make them sink. As saltwater has greater buoyancy, the overshoes must be at least 80% of the weight of the “client” to ensure that the “client” always sinks to the bottom (e.g., a 100-pound client needs an overshoe that weighs a minimum of 80 pounds). While we want a one-size-fits-all product, we still want to make them as light as possible to save materials. Therefore, we must determine the lightest overshoe that will make the heaviest conceivable client sink. We must also factor in whether the application is salt or fresh water. Moreover, working with the customer, Marketing has taken a sample of 48 clients’ weights and recorded the values below. The weights of saltwater clients must be considered separately from freshwater ones. As the clients must always sink, our sample of forty-eight clients cannot possibly encompass the weights of every realistically conceivable client. Therefore, we must use statistics. For our purposes, we will use the sample data to estimate the weight of every realistically conceivable client. We need to be 99.99% confident (i.e., 4 standard deviations) in our client weight projections.

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Step 1: From the given table, segregate salt and fresh water values as shown in the below table (spreadsheet image)

Step 2: Find the values of mean, standard deviation, maximum weight and minimum allowable weight using the formulas highlighted in blue. Answers are highlighted in yellow.

For Fresh water clients,

• The mean is found to be 198.17
• The Standard deviation is found to be 65.71
• Maximum weight is found to be 351
• Minimum allowable weight is found to be 125

For Salt water clients,

• The mean is found to be 222.21
• The Standard deviation is found to be 28.85
• Maximum weight is found to be 288
• Minimum allowable weight is found to be 159

Note: Since I created this as a table in a spreadsheet, took a screenshot from the excel. Directly viewing the answer might not be clear. To view this answer clearly, right click on the answer image and save it to your desktop, so they are very clear and legible…