Final answer:
To determine the value of k in the probability statement P(1.319 < t < k), we use the Student's t-distribution with 23 degrees of freedom, find the cumulative probability up to t = 1.319, and then determine k for the cumulative probability adding the desired interval probability.
Step-by-step explanation:
The student is working with Student's t-distribution to find a probability associated with a range for a t-score in a statistics question. Since the sample size is 24, the degrees of freedom (df) is 23. To find the value of k such that P(1.319 < t < k), we first need to find the probability associated with t = 1.319 for df = 23.
This value can be found in a t-distribution table or using statistical software. Once that probability is determined, we can adjust it to find the cumulative probability up to that point.
To find the value of k, we search for the value on the t-distribution with df = 23 that corresponds to the cumulative probability previously found plus the desired probability for this interval.