The t distribution
A) is smoother than the normal distribution.
B) is quite different from the normal distribution.
C) approaches the normal distribution as its degrees of freedom increase.
D) is necessary when we know the population standard deviation.

Question

Quizplus · Accepted Answer

The t distribution is quite similar to the normal distribution, but with heavier tails. However, as the degrees of freedom (sample size minus one) increase, the t distribution approaches the normal distribution. Therefore, option C is the correct choice. Option A is incorrect because the smoothness of a distribution is subjective and not a defining characteristic. Option B is incorrect because the t distribution is still a bell-shaped curve like the normal distribution. Option D is incorrect because the t distribution is actually used in situations where the population standard deviation is unknown and needs to be estimated from the sample.

The T Distribution