Question

1. For a t distribution with a sample size of 17, find the probability in each region.

1. To the right of 2.120.
2. To the left of 1.337.
3. To the left of -1.746.
4. To the right of 2.583.
5. Between -2.120 and 2.120.
6. Between -1.746 and 1.746.

Answer 1

df = 17 - 1 = 16

a) P(T > 2.120)

= 1 - P(T < 2.120)

= 1 - 0.9750

= 0.0250

b) P(T < 1.337) = 0.9000

c) P(T < -1.746) = 0.0500

d) P(T > 2.583)

= 1 - P(T < 2.583)

= 1 - 0.9900

= 0.0100

e) P(-2.120 < T < 2.120)

= P(T < 2.120) - P(T < -2.120)

= 0.9750 - 0.0250

= 0.9500

f) P(-1.746 < T < 1.746)

= P(T < 1.746) - P(T < -1.746)

= 0.9500 - 0.0500

= 0.9000