A company maintains three offices in a certain region, each staffed bytwo employees. Information concerning yearly salaries (1000s of dollars)is as follows: Office 1 1 2 2 3 3 Employee 1 2 3 4 5 6 Salary 29.7 33.6 30.2 33.6 25.8 29.7 a. Suppose two of these employees are randomly selected fromamong the six (without replacement). Determine the samplingdistribution of the sample mean salary x̄. b. Suppose one of the three offices is randomly selected. LetX1 and X2 denote the salaries of the two employees.Determine the sampling distribution of x̄.c. How does E(x̄ )from parts (a) and (b) compare to thepopulation mean salary µ?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
A company maintains three offices in a certain region, each staffed by
two employees. Information concerning yearly salaries (1000s of dollars)
is as follows:
| Office | 1 | 1 | 2 | 2 | 3 | 3 |
| Employee | 1 | 2 | 3 | 4 | 5 | 6 |
| Salary | 29.7 | 33.6 | 30.2 | 33.6 | 25.8 | 29.7 |
a. Suppose two of these employees are randomly selected from
among the six (without replacement). Determine the sampling
distribution of the sample
b. Suppose one of the three offices is randomly selected. Let
X1 and X2 denote the salaries of the two employees.
Determine the sampling distribution of x̄.
c. How does E(x̄ )from parts (a) and (b) compare to the
population mean salary µ?
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