Concrete Thickness a Roadway Construction Process Uses a Machine That

question 119

Essay

Concrete thickness A roadway construction process uses a machine that pours concrete onto the roadway and measures the thickness 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 inch 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 described 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 standard deviation must they attain?
c. Explain what achieving a smaller standard deviation means in this context.

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Definitions:

Technological Advance

It refers to the development and application of new technologies and innovation, which can improve efficiency, productivity, and capabilities in various sectors.

Per Capita Outputs

The average output produced per person in a given area or country, often used as a measure of productivity or economic performance.

Saving and Investment

Refers to the act of setting aside funds for future use and the use of those funds to create assets expected to generate returns over time.

Technological Advance

The development and application of new technologies and methods, improving efficiency, productivity, or creating new products.