A Precision Control Engineer Is Interested in the Mean Length $\alpha$

question 107

Essay

A precision control engineer is interested in the mean length of tubing being cut automatically by machine.It is known that the standard deviation in the cutting length is 0.15 feet.A sample of 60 cut tubes yields a mean length of 12.15 feet.This sample will be used to obtain a 99% confidence interval for the mean length cut by machine.
a.What is the z $\alpha$ / 2 value to use in obtaining the confidence interval?
b.Develop the 99% confidence interval for $\mu$ .

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Definitions:

Initiating Structure

Leadership behavior focused on defining and organizing work tasks, roles, and responsibilities clearly.

Team

A group of individuals working together to achieve a common goal, often characterized by shared responsibilities and collaborative effort.

Task Behaviors

Actions focused on getting the job done, including planning, organizing, and executing tasks.

Initiating Structure

A leadership behavior that emphasizes the organization of work, work roles, and work activities, focusing on task-oriented goals.