Final answer:
The questions relate to statistical operations such as calculating means and standard deviations, constructing probability distributions, assessing event probabilities, and conducting hypothesis tests. These activities fall under the subject of college-level Mathematics.
Step-by-step explanation:
The questions presented involve statistical concepts that are typically covered in college-level mathematics, specifically in the area of statistics. For instance, calculating the mean and standard deviation of the number of births per hour in a maternity ward, constructing probability distributions, and assessing probabilities of certain events are all statistical exercises. Furthermore, conducting a hypothesis test concerning the average number of babies on flights based on survey data requires understanding of statistical inference methods.
A specific example involves the maternity ward at a hospital in the Philippines, where the average number of births per day is 60. To find the mean number of births per hour, X, one would divide 60 by the number of hours in a day, which would result in a mean (μ) of 2.5 births per hour. If the births are uniformly distributed and independent, the standard deviation (σ) can be calculated using the formula for the standard deviation of a uniform distribution. A graph of the probability distribution of X could be a histogram showing the frequencies of different numbers of births per hour over a period of time. For the probability calculations, if we assume a Poisson distribution due to the nature of the event (births), we can calculate the probability of three births in an hour using the Poisson probability function.