Question

1. which of the following is a true statement? (select only one)

(a) the area under a normal curve is always equal to 100%, no matter what the mean and standard deviation are.
(b) all bell - shaped curves are skewed distributions.
(c) the smaller the standard deviation of a normal curve, the lower and more spread out the graph.
(d) your data must follow a density curve exactly in order to use normal approximations.
(e) if the standard deviation of your normal distribution is smaller than 1, you cannot use the standard normal curve to approximate percentages.

Explanation:

• Option A: The total area under a normal curve represents the total probability of all possible outcomes, which is always 1 or 100% regardless of mean and standard - deviation values.
• Option B: Bell - shaped curves can be symmetric (like the normal distribution) and not all are skewed.
• Option C: A smaller standard deviation makes the normal curve taller and narrower, not lower and more spread out.
• Option D: Normal approximations can be used even when data doesn't follow a density curve exactly.
• Option E: The standard normal curve can be used for any normal distribution regardless of the standard deviation value.

Answer:

A. The area under a normal curve is always equal to 100%, no matter what the mean and standard deviation are.