Final answer:
The question involves expressing the concept of a normal distribution in Mathematics. X would represent the weight of an item following that distribution with a given mean and standard deviation. The question involves sketching a normal distribution curve, labeling the mean, and points representing 1, 2, and 3 standard deviations from the mean.
Step-by-step explanation:
The question pertains to normal distributions, which is a concept in statistics under the subject of Mathematics, and relates to the college level wherein students learn about probability distributions and statistical analysis.
In terms of the normal distribution, the random variable X would generally be defined as the weight of an item from a population that follows a normal distribution with a specified mean and standard deviation. For instance, if we're talking about the weight of bags of potato chips, X would represent the weight of a potato chip bag.
The distribution is symmetric about a vertical line drawn through the mean, denoted by μ (mu). The mean, median, and mode all coincide in a perfectly normal distribution, and the shape of the distribution is solely determined by its mean and standard deviation. An increase or decrease in the standard deviation will make the curve fatter or skinnier, while a change in the mean shifts the curve to the left or right. Drawing the normal distribution graph and labeling it appropriately would involve marking the mean at 9.12 ounces and noting the points 1, 2, and 3 standard deviations away from the mean, at 9.17, 9.22, and 9.27 ounces, as well as 9.07, 9.02, and 8.97 ounces, respectively.