Final answer:
In statistics, the exponential distribution best describes a scenario where the number of occurrences exponentially decreases as the value increases, such as the ability to run longer distances. Most hypothesis tests in statistics default to using the normal distribution, which is bell-shaped and defined by its mean and standard deviation. The standard normal distribution is a specific normal distribution with a mean of zero and standard deviation of one.
Step-by-step explanation:
The subject of the question appears to revolve around the properties and applications of different statistical distributions, specifically the assumption that stock prices are lognormally distributed. When looking at the example provided, which describes a situation where many people can run short distances but fewer can run longer distances, the distribution that fits this scenario is the exponential distribution. This is because in an exponential distribution, the likelihood of larger values decreases exponentially. Hence, as the running distance increases, fewer people can run that distance.
Conducting hypothesis tests often involves identifying the correct statistical distribution. For many hypothesis tests, the normal distribution is used, particularly when the sample size is large enough for the central limit theorem to apply, or when the population distribution is known to be normal. Additionally, the normal distribution is the most widely used distribution in various disciplines, and it is defined by its mean (μ) and standard deviation (σ). A special case, the standard normal distribution, deals exclusively with z-scores and has a mean of zero and standard deviation of one.