Brian is playing a carnival game. He is blindfolded while he throws a dart at a board of 12 balloons, as shown below. Each balloon is labeled "S" for small, "M" for medium, "L" for large, or "XL" for extra-large. The board has 3 small balloons, 5 medium balloons, 2 large balloons, and 2 extra-large balloons. He hits one of the balloons at random and wins a stuffed animal of that size.

Determine if the following statement is true or false. the normal curve is symmetric about its​ mean, mu. choose the best answer below. a. the statement is false. the normal curve is not symmetric about its​ mean, because the mean is the balancing point of the graph of the distribution. the median is the point where​ 50% of the area under the distribution is to the left and​ 50% to the right.​ therefore, the normal curve could only be symmetric about its​ median, not about its mean. b. the statement is true. the normal curve is a symmetric distribution with one​ peak, which means the​ mean, median, and mode are all equal.​ therefore, the normal curve is symmetric about the​ mean, mu. c. the statement is false. the mean is the balancing point for the graph of a​ distribution, and​ therefore, it is impossible for any distribution to be symmetric about the mean. d. the statement is true. the mean is the balancing point for the graph of a​ distribution, and​ therefore, all distributions are symmetric about the mean.