(a)Consider a t distribution with 20 degrees of freedom. Compute P≥t−1.12. Round your answer to at least three decimal places.P≥t−1.12=(b)Consider a t distribution with 14 degrees of freedom. Find the value of c such that =P<−c<tc0.90. Round your answer to at least three decimal places.c=

(a) To compute P≥t−1.12 for a t-distribution with 20 degrees of freedom, we need to find the area to the right of t=-1.12 on the t-distribution curve. This is equivalent to finding 1 - P(t < -1.12).

You can use a t-distribution table or statistical software to find this probability. For a t-distribution with 20 degrees of freedom, the probability P(t < -1.12) is approximately 0.1379.

So, P≥t−1.12 = 1 - P(t < -1.12) = 1 - 0.1379 = 0.8621.

So, P≥t−1.12 is approximately 0.862, rounded to three decimal places.

(b) To find the value of c such that P<−c<tc=0.90 for a t-distribution with 14 degrees of freedom, we need to find the t-value that leaves 0.90 area in the middle of the t-distribution curve, and 0.05 in each tail (because 1 - 0.90 = 0.10, and this area is split equally between the two tails).

You can use a t-distribution table or statistical software to find this t-value. For a t-distribution with 14 degrees of freedom, the t-value that leaves 0.05 in the tail is approximately 1.761.

So, c is approximately 1.761, rounded to three decimal places.