Which of the following are correct?
(A) The probability curve in t-distribution is symmetric about the line \(t = 0\).
(B) t-axis is an asymptote of the curve.
(C) The variable t of t-distribution ranges from \(-\infty\) to \(\infty\)
(D) As the number of degrees of freedom increases, the t-distribution curve moves closer to the binomial distribution.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (C) only
The t-distribution is a bell-shaped, continuous distribution, flatter than the normal curve, and it approaches the normal distribution as the degrees of freedom grow.
Checking the statements
(A) The probability curve in t-distribution is symmetric about the line \(t = 0\). — Correct. Its density depends on \(t^2\), so the values at t and \(-t\) are equal.
(B) t-axis is an asymptote of the curve. — Correct. The two tails come closer and closer to the t-axis but never touch it.
(C) The variable t of t-distribution ranges from \(-\infty\) to \(\infty\) — Correct. t can take every real value.
(D) As the number of degrees of freedom increases, the t-distribution curve moves closer to the binomial distribution. — Incorrect. For large degrees of freedom the t-curve approaches the standard normal curve, not the binomial distribution (which is discrete).