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Which property correctly describes how the Student's t-distribution compares to the standard normal distribution?
AIt has more probability in its tails, so it is flatter in the center
BIt has less probability in its tails, so it is taller in the center
CIt is skewed strongly to the right for every sample size
DIt only takes on positive values, unlike the normal distribution
Answer & Solution
Correct answer: A. It has more probability in its tails, so it is flatter in the center
1. Several properties compare the two distributions.
2. Because the t-distribution's spread is greater than the normal's, it places more probability out in its tails.
3. That extra tail weight comes from somewhere, so the t-distribution is correspondingly flatter and shorter in the center than the normal curve.
4. Options C and D describe skewness and a positive-only range, neither of which is a real property of the symmetric t-distribution.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.2 A Single Population Mean using the Student t Distribution_
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