The Normal Probability Distribution: Please Answer Below T

The Normal Probability Distributionplease Answer The Below Two Questio

The Normal Probability Distributionplease Answer The Below Two Questio

The Normal Probability Distribution Please answer the below two question, font new Times Roman 12- in about two hundred words In §6.2 we are introduced to the Normal Probability Distribution and the special case of the Normal Probability Distribution, the Standard Normal Probability Distribution, which is a Normal Probability Distribution with mean ( u ) zero and variance (σ2) one. One way to find probabilities from a Standard Normal Distribution is to use probability tables, which are located inside the front cover of your textbook. · According to the table, what is the probability when z ≤ -1.75? The probability when z ≤ 1.75? · What properties of probability distributions and specifically the Normal Probability Distribution do you notice from the two probabilities that you have found in the table?

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The Standard Normal Distribution is a critical concept in statistics, representing a Normal Distribution with a mean of zero and a variance of one. Utilizing z-scores allows us to find probabilities associated with data points relative to this distribution. According to the probability table in the textbook, the probability when z ≤ -1.75 is approximately 0.0401, meaning there is about a 4.01% chance that a randomly selected value falls below this z-score. Conversely, the probability when z ≤ 1.75 is approximately 0.9599, indicating a 95.99% chance that a value falls below this point. These probabilities demonstrate that the distribution is symmetric around the mean, with roughly 95% of data within ±1.75 standard deviations of the mean. From these values, it is evident that the normal distribution has continuous symmetry, and the probabilities increase symmetrically as z moves from negative to positive, reflecting the key property of the normal curve being bell-shaped with equal tails on either side. Such properties make the Normal Distribution essential for inferential statistics, especially in assessing probabilities and setting confidence intervals.

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