Final answer:
The student's question is a probability problem that seems related to the hypergeometric distribution, but the specific question lacks context. Examples given demonstrate calculating probabilities and expected values within a hypergeometric context, such as determining the expected number of non-technically proficient members on a committee.
Step-by-step explanation:
The student's question appears to be a probability problem related to the hypergeometric distribution. However, the actual probability question (the likelihood that at least three employees are not members of a labor organization when randomly selecting eight employees) has not been provided with enough context or information to solve. Therefore, we will instead address the provided samples and information related to probability.
For the example of selecting 30 employees from a workforce of 150, the chance of any one employee being chosen changes each time an employee is selected without replacement. Initially, the chance of being picked is 30 out of 150. After one employee is selected, it reduces to 29 out of 149, and so on.
With the technology task force example, the random variable X can be defined as the number of individuals who are not technically proficient among the 10 people chosen for the committee. To find the expected number of instructors who are not technically proficient, you would use the expected value formula for hypergeometric distribution. In this case, the expected number is calculated as: (10 * 8) / 28.
Using hypergeometric probability formulas, we can find the probability that at least five on the committee are not technically proficient, and the probability that at most three on the committee are not technically proficient. Each of these probabilities would be calculated considering the population, the number of successes in the population, the sample size, and the number of successes in the sample.