Suppose That the Starting Salaries of Male Workers Are Normally $\bar { X } _ { 1 }$

question 7

Essay

Suppose that the starting salaries of male workers are normally distributed with a mean of $56 000 and a standard deviation of $12 000. The starting salaries of female workers are normally distributed with a mean of $50 000 and a standard deviation of $10 000. A random sample of 50 male workers and a random sample of 40 female workers are selected.
a. What is the sampling distribution of the sample mean difference $\bar { X } _ { 1 }$ - $\bar { X } _ { 2 }$ ? Explain.
b. Find the expected value and the standard error of the sample mean difference.
c. What is the probability that the sample mean salary of female workers will not exceed that of the male workers?

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Definitions:

Fixed Cost

Expenses that do not change with the level of production or sales, such as rent, salaries, and insurance, remaining constant regardless of business activity volume.

Patent

A legal document granting an inventor exclusive rights to manufacture, use, or sell an invention for a certain number of years.

Demand Schedule

A table that shows the quantity of a good or service that consumers are willing and able to purchase at various prices during a specified period of time.

Marginal Cost

The increase in total cost that arises from an extra unit of production.