A three part Stats problem Help

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In summary, the conversation discusses the process of measuring the thickness of concrete in a roadway construction project using a machine that has a standard deviation of 1.75 inches. The company sets the machine to average 26 inches for the batches of concrete and is concerned about the percentage of concrete that falls below the minimum required depth of 23 inches. To meet the requirement of having only 3% of the output under the limit, the company's lawyers suggest reducing the standard deviation. This means finding the probability of a value being less than a certain point, using the normal distribution table and adjusting for the mean and standard deviation of the machine's output.
  • #1
Dani16
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-I have no clue where to start-

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A roadway construction process uses a machine that pours concrete onto the roadway and measures the thinckness of the concrete so the roadway will measure up to the required depth in inches. The concrete thickness needs to be consistent across the road, but the machine isn't perfect and it is costly to operate. Since there's a safety hazard if the roadway is thinner than the minimum 23 inches thickness, the company sets the machine to average 26 inches for the batches of concrete. They believe the thickness level of the machine's concrete output can be decribed by a normal model with standard deviation 1.75 inches. [show work]

a) What percent of the concrete roadway is under the minimum depth ?


b) The company's lawyers insist that no more than 3% of the output be under the limit. Because of the expense of operating the machine, they cannot afford to reset the mean to a higher value. Instead they will try to reduce the standard deviation to achieve the "only 3% under" goal. What SD must they attain?


c) Explain what achieving a smaller standard deviation means in this context.




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I thought that you would draw out the normal model, but after that I really have no clue what to do. Please Help me !
 
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  • #2
Somewhere in your textbook there is a table of the Normal Distribution. Find it. You are going to need it. The table is adjusted for a mean of 0 and a standard deviation of 1. Obviously, that is not your mean or standard deviation so you will have to fix that. The way you do that is as follows where a is your value that you are trying to find the probability of:

P{x <= a} = G((a-mean)/standard deviation). Then you look up the number you have inside G() in the table.

Some tricks:

1. G(-x) = 1-G(x)

2. The table may or may not want you to add 1/2 to the values. If it starts off at 1/2 then you don't have to. If it doesn't then add 1/2.

Try your problem now, write down what you do and I or someone else will help you...
 
  • #3


Hello, as a scientist, I would be happy to help you with this statistics problem. Let's break it down into three parts and work through it step by step.

a) To answer this question, we need to find the area under the normal curve that represents the concrete thickness being less than 23 inches. This can be done using a standard normal table or a calculator that has a normal distribution function. Using a standard normal table, we find that the area to the left of 23 inches is 0.0918 or approximately 9.18%. This means that 9.18% of the concrete roadway is under the minimum depth of 23 inches.

b) To answer this part, we need to find the standard deviation that will result in only 3% of the output being under the minimum depth. We can use the same method as in part a) but this time, we need to find the z-score that corresponds to 3% in the standard normal table. We find that the z-score is -1.88. We can then use the formula z = (x - μ) / σ where z is the z-score, x is the value we are trying to find (in this case, the standard deviation), μ is the mean, and σ is the standard deviation. Rearranging the formula to solve for σ, we get σ = (x - μ) / z. Plugging in the values, we get σ = (23 - 26) / -1.88 = 1.59 inches. This means that the company must attain a standard deviation of 1.59 inches to achieve the "only 3% under" goal.

c) Achieving a smaller standard deviation means that the data points (concrete thickness measurements) will be closer to the mean. In this context, it means that the variability in concrete thickness will be reduced, resulting in a more consistent thickness across the roadway. This can help the company save on costs as they will not be wasting concrete by pouring batches that are too thin and they will also reduce the risk of safety hazards due to thinner roadways.

I hope this explanation helps you understand the problem better. If you have any further questions, please don't hesitate to ask. Good luck!
 

What are the three parts of a statistics problem?

The three parts of a statistics problem are the question or hypothesis, the data or information needed to answer the question, and the analysis and interpretation of the data.

Why is it important to break down a statistics problem into three parts?

Breaking down a statistics problem into three parts helps to clarify the question being asked, identify the relevant data, and organize the steps needed to solve the problem. This approach also helps to avoid confusion and errors in the analysis.

What are the common challenges in solving a three part statistics problem?

Some common challenges in solving a three part statistics problem include identifying the appropriate data to use, understanding the underlying concepts and assumptions, and choosing the right statistical methods to use in the analysis.

How can I improve my skills in solving three part statistics problems?

To improve your skills in solving three part statistics problems, you can practice with different types of problems, seek help from a tutor or mentor, and familiarize yourself with statistical software and tools. It is also important to understand the underlying concepts and theories behind the methods used in statistics.

What are some real-world applications of solving three part statistics problems?

Solving three part statistics problems is essential in many fields such as business, economics, social sciences, and healthcare. Examples of real-world applications include analyzing market trends, evaluating the effectiveness of a new drug, and predicting the success of a marketing campaign.

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