Respuesta :
Answer:
True
Step-by-step explanation:
The percentages or areas under the normal curve can indeed be interpreted as probabilities. The normal distribution, also known as the Gaussian distribution or bell curve, is characterized by its probability density function, and areas under the curve correspond to probabilities of certain events occurring within specific ranges.
Final answer:
True, the percentages or areas under the normal curve represent probabilities as it is a probability density function, with areas corresponding to the likelihood of outcomes within specified intervals.
Explanation:
The statement is true: the percentages or areas under the normal curve can be interpreted as probabilities. This is because the normal curve represents a probability density function (PDF), where the total area under the curve is equal to 1, or 100%, signifying the entirety of possible outcomes. Understanding this is fundamental to grasping concepts in statistics and probability theory.
When we consider empirical or theoretical probabilities, we're either observing real-life events or basing predictions on a set of rules, respectively. For example, if a probability density function reflects that the area under the curve between two points a and b is 0.25, we interpret this as a probability of 25%. That means, when drawing many samples from the distribution, approximately 25% will fall between a and b.
A practical application of this concept is in constructing confidence intervals. If we say that 95 percent of all confidence intervals contain the true population mean, then we are referring to the area under the curve of the probability distribution corresponding to the 95% confidence level. Similarly, with a die, we use a probability distribution graph to show that the sum of probabilities for all outcomes adds up to 1, and the area corresponding to each outcome represents its probability; in the case of a fair die, this is 1/6 per side.
