Question

Which of the following statements are true? There may be more than one correct statement; check all that are true. a) The t distribution is a discrete probability distribution. b) The t distribution tends toward the standard normal distribution as the degrees of freedom increase. c) The t distribution is right skewed unless the degrees of freedom are very large. d) A random variable that has a t distribution cannot take on negative values.

Answer 1

Answer: Choice B only

Step-by-step explanation:

Let's go over the possible choices to see which statements are true and which are false.

• a) This is false. The T distribution is continuous.
• b) This is true. When n > 30, the T distribution looks a lot like the standard normal Z distribution. The difference between the two becomes negligible. This is why you're able to use the Z distribution if n > 30, even if you don't know sigma.
• c) This is false. The T distribution is symmetric for any degrees of freedom value.
• d) This is false. Negative values are possible in a T distribution.

To summarize, only choice B is true. The rest are false.