Final answer:
To draw and label the normal curve based on the given information, a bell-shaped curve is centered at the mean of 106 on the x-axis, marking the mean, median, and mode, with intervals at 104 and 108 representing one standard deviation away from the mean.
Step-by-step explanation:
The question pertains to understanding the properties of a normal distribution and involves several scenarios where this knowledge is applied. For instance, a plant manager is considering recalibration of equipment based on the standard deviation of weights, a company examines the plausibility of claims about the diameters of screws, and a biology class assesses exam scores using z-scores. In discussing a normal distribution, it is significant to know that it is symmetrical about the mean, which is also the median and mode.
To answer the student's question specifically on how to draw and label the normal curve, you would sketch a symmetrical bell-shaped curve centered at the mean value of 106 with markings along the horizontal axis to denote standard deviations from the mean. The standard deviation intervals would be at 104, 106, and 108, marking one standard deviation below, at, and above the mean respectively, assuming a depiction where the standard deviation is represented as 2 units on the graph.
In terms of theoretical distribution, standard normal distribution, and z-scores, these topics illustrate how data can be standardized and compared. The median of a normal distribution with a mean of 61 and a standard deviation of 15 is also 61, since for normal distributions mean = median = mode.