Question

Which of the following statements are false? I. The standard normal table can be used with z scores from any distribution. II. The mean is always equal to the median for any normal distribution. III. Every symmetric, bell shaped distribution is normal. IV. The area under a bell curve is always 1, regardless of the mean and standard deviation

Answer 1

The mean is not always equal to the median for any normal distribution, and not all symmetric, bell-shaped distributions are normal.

Step-by-step explanation:

The false statements are II. The mean is always equal to the median for any normal distribution, and III. Every symmetric, bell-shaped distribution is normal.

For statement II, it is not true that the mean is always equal to the median for any normal distribution. While a normal distribution is symmetric and the mean, median, and mode are all located at the same point, this does not hold true for all distributions.

For statement III, it is not true that every symmetric, bell-shaped distribution is normal. While a normal distribution is symmetric and bell-shaped, not all are symmetric, bell-shaped distributions are normal. There are other distributions, such as the Student's t-distribution or the logistic distribution, that are also symmetric and bell-shaped.