Final answer:
The shape of the normal curve in a normal distribution is controlled by its standard deviation, while the location of the curve's peak is determined by its mean. The curve is symmetric with equal mean, median, and mode. So the correct answer is option C.
Step-by-step explanation:
When describing elements of the normal distribution, it is essential to understand that it is defined by its mean (μ) and standard deviation (σ). The shape of the normal curve is related to these two parameters. Specifically, the mean determines the location of the center of the curve, which is also the peak since the mean, median, and mode coincide in a perfectly symmetrical, bell-shaped distribution. The standard deviation, on the other hand, controls the spread or width of the curve, determining how much the data values deviate from the mean.
Among the listed statements about the shape of a normally distributed data set, the true statement is:
c.) The shape of the normal curve is controlled by the standard deviation of the data.