Question

in the t-distribution with sample size n = 30, what is the probability that t < 2.000? give answer to 3 decimals.

Explanation:

Step1: Determine degrees of freedom

Degrees of freedom \( df = n - 1 = 30 - 1 = 29 \).

Step2: Use t - distribution table or calculator

We want to find \( P(t < 2.000) \) for \( df = 29 \). Using a t - distribution calculator or table, we know that the t - distribution is symmetric around 0. The probability that \( t<2.000 \) can be found by looking up the cumulative probability for \( t = 2.000 \) with \( df=29 \). From t - distribution tables or statistical software, we find that \( P(t < 2.000)\approx0.975 \) (more precisely, using a calculator, the cumulative probability for \( t = 2.000 \) and \( df = 29 \) is approximately 0.975 when rounded to three decimal places).

Answer:

\( 0.975 \)