MNM Corporation Gives Each of Its Employees an Aptitude Test $\bar{x}$

question 31

Essay

MNM Corporation gives each of its employees an aptitude test.The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15.A simple random sample of 25 is taken from a population of 500.
a.What are the expected value,the standard deviation,and the shape of the sampling distribution of $\bar{x}$ ?
b.What is the probability that the average aptitude test in the sample will be between 70.14 and 82.14?
c.What is the probability that the average aptitude test in the sample will be greater than 82.68?
d.What is the probability that the average aptitude test in the sample will be less than 78.69?
e.Find a value,C,such that P( $\bar{x}$ $\ge$ C)= .015.

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Definitions:

Price to Clear

The price to clear is the market price at which the quantity supplied equals the quantity demanded, thereby clearing the market without leaving surplus or shortage.

Perfectly Competitive Industry

A Perfectly Competitive Industry is characterized by many sellers and buyers, free entry and exit, and a product that is identical across suppliers, leading to no single entity having market control.

Marginal Cost

The additional cost of producing one extra unit of a good or service.

Total Revenue

The total amount of money a company receives from selling its goods or services before any expenses are subtracted.