Final answer:
The normal distribution is symmetric and bell-shaped with equal mean, median, and mode, and is not skewed.
Step-by-step explanation:
The true statements about the normal distribution are: It is symmetrical, the mean, median, and mode are equal, and it is bell-shaped.The normal distribution is a fundamental concept in the field of statistics. It is characterized by a symmetric, bell-shaped curve where the mean, median, and mode all coincide at the center. This means the distribution is not skewed; rather, it is perfectly balanced on either side of the central value. The areas under the curve represent probability and the total area equals 1, adhering to the probability theory.
Furthermore, according to the Empirical Rule, specific percentages of data fall within one, two, or three standard deviations from the mean, highlighting the predictability and consistency of the normal distribution.It is symmetrical: The normal distribution is symmetrical, which means that it is evenly balanced on both sides of the mean.The mean, median, and mode are equal: In a normal distribution, the mean, median, and mode are all equalIt is positively skewed: This statement is false. The normal distribution is not positively skewed. It has a bell-shaped curve with no skewnessIt is bell-shaped: The normal distribution is characterized by a bell-shaped curve, which means that the majority of the data falls near the mean, with fewer data points in the tails.Therefore, the true statements about the normal distribution are A, B, and D.