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Chapter 8: Q 8.144. (page 345)

Let 0<伪<1. For a t-curve, determine

a. the t-value having area 伪to its right in terms of t伪

b. the t-value having area 伪 to its left in terms of t伪

c. the two t-values that divide the area under the curve into a middle 1-伪area and two outside 伪/2areas.

d. Draw graphs to illustrate your results in parts (a)-(c).

Short Answer

Expert verified

Part (a) The graph is

Part (b) The graph is

Part (c) The graph is

Step by step solution

01

Part (a) Step 1: Given information

0<伪<1

02

Part (a) Step 2: Explanation

For a t=curve, the t-value having area 伪 to its right is t伪

03

Part (b) Step 1: Explanation

Because the t-curve is symmetric about 0, the t-value with area 伪to its left is equal to the negative of the t-value with area 伪to its right.

鈭�The t-value having area 伪to its left

=-(t-value having area 伪to its right )

=-t伪

04

Part (c) Step 1: Explanation

To obtain the two t-values that divide the curve's area into two halves 1-伪area and two outside 伪2areas i.e., to obtain two t-values such that one of it, has area 伪2to its right and the other has area 伪2to its left.

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