Final answer:
The question deals with the application of probability and statistics concepts to scenarios involving physics and engineering majors at a university.
Step-by-step explanation:
The student's question pertains to the field of probability and statistics for engineering and the sciences. This involves determining the likelihood of various scenarios and understanding data distributions, means, and standard deviations. In the context provided, the student is asked to work with a probability distribution pertaining to physics majors involved in postgraduate research, and another scenario involving the selection of engineering majors at a university. To answer these questions involves calculating probabilities using the given data and statistical methods.
For the first scenario, the professor will use the probability distribution to ascertain what percent of physics majors will engage in postgraduate research. The probability distribution of X in the second scenario describes the probability of each possible outcome in selecting students until an engineering major is found. To find the mean of X, you would divide 1 by the given probability of finding an engineering major, and for the standard deviation of X, you would calculate the square root of the variance of X.
Regarding the hypergeometric distribution question, this would involve determining whether the scenario of selecting a sample of students from a group meets the criteria of hypergeometric experiments. The conditions typically include a set population size, a specific number of successes within the population, and a sample that is drawn without replacement.