A Machine Is Used in a Production Process

question 101

Short Answer

A machine is used in a production process. From past data, it is known that 97% of the time the machine is set up correctly. Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable (non-defective) items. However, when it is set up incorrectly, it produces only 40% acceptable items.
a.An item from the production line is selected. What is the probability that the selected item is non-defective?
b.Given that the selected item is non-defective, what is the probability that the machine is set up correctly?

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Definitions:

Total Income

The sum of all earnings or revenue received by an individual or an entity, including wages, profits, rents, and other forms of earnings.

Capitalists

Individuals or entities that own capital goods or investments, and use these to produce goods and services for profit.

Rent

A regular payment made by tenants to landlords for the use of property or land; in economics, it also refers to earnings in excess of the minimum amount necessary to keep a factor of production in its current use.

Proprietor's Income

Income earned by the owner of a sole proprietorship from the business's net earnings.