Given a variable that has at distribution with the specified degrees of freedom, what percentage of the time will its value fall in the indicated region? (Round your answers to one decimal place.)
(a) 10 df, between - 1.37 and 1.37

(b) 10 df, between -3.17 and 3.17

(c) 24 df, between-2.49 and 2.49

Question

18-09-2025
Mathematics

High School

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Given a variable that has at distribution with the specified degrees of freedom, what percentage of the time will its value fall in the indicated region? (Round your answers to one decimal place.)
(a) 10 df, between - 1.37 and 1.37

(b) 10 df, between -3.17 and 3.17

(c) 24 df, between-2.49 and 2.49

Answer :

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reetukatiyar26 reetukatiyar26 · Answer 1 · 2024-04-15T13:37:22-04:00

Final answer:

To find the percentage of the time a value falls within a given region in a distribution with specified degrees of freedom, you need to use the t-distribution. The percentages for the provided regions are approximately 86.7%, 98.8%, and 96.2% for (a), (b), and (c) respectively.

Explanation:

To find the percentage of the time a value falls within a given region in a distribution with specified degrees of freedom, you need to use the t-distribution. In this case, we have three different scenarios:

a) For 10 degrees of freedom, the t-value for a two-tailed test with a 95% confidence level is 2.228. The region between -1.37 and 1.37 corresponds to -1.37 < t < 1.37. Using a t-table or calculator, we find that the area under the curve is approximately 86.7%.

b) For 10 degrees of freedom, the region between -3.17 and 3.17 corresponds to -3.17 < t < 3.17. Using a t-table or calculator, we find that the area under the curve is approximately 98.8%.

c) For 24 degrees of freedom, the region between -2.49 and 2.49 corresponds to -2.49 < t < 2.49. Using a t-table or calculator, we find that the area under the curve is approximately 96.2%.