Final answer:
Larger standard deviations result in a wider or "fatter" normal curve but do not affect its skewness; the normal curve remains symmetrical regardless of standard deviation size.
Step-by-step explanation:
Larger values of the standard deviation indicate a greater variability within a dataset. In the context of a normal curve, which is a type of probability distribution, larger standard deviations result in a curve that is wider or "fatter," but remains symmetrical. It's important to note that standard deviation does not affect the skewness of the distribution—a normal curve is always symmetrical, regardless of the value of the standard deviation. Therefore, larger standard deviations do not result in a normal curve that is skewed to the left or to the right.
Skewness is a separate measurement that indicates the asymmetry of a distribution. It can be to the left (negative skew) or to the right (positive skew). For a normal curve, skewness is zero because the distribution is perfectly symmetrical, with the mean, median, and mode all located at the center.
In conclusion, larger values of the standard deviation result in a normal curve that is symmetrical (Option 3).