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What is the probability for a t distribution with 18 degrees of freedom, for each specified region? (Round your answers to three decimal places if needed.)

a) The probability that t is less than -2.101
b) The probability that t is greater than 1.734
c) The probability that t is between -1.734 and 1.734
d) The probability that t is greater than -2.101

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Final answer:

The probability for a t distribution with 18 degrees of freedom can be found using a probability table or a calculator with the tcdf function, which calculates the probability for given t values and degrees of freedom.

Step-by-step explanation:

The probability for a t distribution with 18 degrees of freedom for the specified regions can be calculated using a probability table or a calculator with functions for the Student's t-distribution, such as the tcdf command on a TI-83, 83+, and 84+ calculator. The given t scores can be looked up or calculated as follows:

  • a) For t less than -2.101, you can use the tcdf function to find the probability to the left of -2.101.
  • b) For t greater than 1.734, the probability to the right can be found by subtracting the tcdf output from 1.
  • c) For t between -1.734 and 1.734, the tcdf function will directly give the probability between these two values.
  • d) For t greater than -2.101, again subtract the tcdf output for -2.101 from 1 to find the probability to the right.

Note that the tables or calculator outputs typically give the area under the curve to the left of the given t score. Therefore, we need to be mindful of whether we are looking for the area to the left or right of our t score when interpreting the results.

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