Mathematics, 21.07.2020 18:01 ashleydaya

For a t distribution with 16 degrees of freedom, find the area, or probability, in each region. a. To the right of 2.120. (Use 3 decimals.) b. To the left of 1.337. (Use 2 decimals.) c. To the left of -1.746. (Use 2 decimals.) d. To the right of 2.583. (Use 2 decimals.) e. Between -2.120 and 2.120. (Use 2 decimals.) f. Between -1.746 and 1.746. (Use 2 decimals.)

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The required probabilities using the t-distribution table will be a. 0.025, b. 0.90, c. 0.05, d, 0.01, e. 0.95, and f. 0.90.

Given:

A t-distribution with 16 degrees of freedom.

See the graph for the given distribution.

It is required to calculate the probability of:

a. To the right of 2.120. (Use 3 decimals.) b. To the left of 1.337. (Use 2 decimals.) c. To the left of -1.746. (Use 2 decimals.) d. To the right of 2.583. (Use 2 decimals.) e. Between -2.120 and 2.120. (Use 2 decimals.) f. Between -1.746 and 1.746.

Use the table of t-distribution to calculate the required probabilities.

$P(T_\nut_{\alpha;\nu})=\alpha$ where $\nu$ is the degree of freedom.

The required probabilities will be,

a) To the right of 2.120.

$P(T_{16}2.120)=0.025$

b) To the left of 1.337

$P(T_{16}1.337)\\=1-0.1\\=0.9$

c) To the left of -1.746

$P(T_{16}1.746)\\=0.05$

d) To the right of 2.583.

$P(T_{16}2.583)=0.01$

e) Between -2.120 and 2.120.

P(-2.120

f) Between -1.746 and 1.746.

P(-1.746

Therefore, the required probabilities using the t-distribution table will be a. 0.025, b. 0.90, c. 0.05, d, 0.01, e. 0.95, and f. 0.90.

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Answer from: estherklein15ov3vx9

a. 0.025

b. 0.90

c. 0.05

d. 0.01

e. 0.95

f. 0.90

Step-by-step explanation:

From the T-distribution table, we have;

$Pr(T_v t_{\alpha;v }) = \alpha$

For a t distribution with 16 degrees of freedom, we have;

a. $Pr(T_{16} 2.120 }) = 0.025$

b. $Pr(T_{16} < 1.337}) =1 - Pr(T_{16} 1.337}) = 1 - 0.1 = 0.90$

c. $Pr(T_{16} < -1.746}) =Pr(T_{16} 1.746}) = 0.05$

d. $Pr(T_{16} 2.583}) = 0.01$

e. $Pr(-2.120 < T_{16} < 2.120 }) = 1 - 2 \times Pr(T_{16} 2.120 }) = 1 - 2 \times 0.025 = 0.95$

f. $Pr(-1.746< T_{16} < 1.746}) = 1 - 2 \times Pr(T_{16} 1.746}) = 1 - 2 \times 0.05 = 0.90$

For a t distribution with 16 degrees of freedom, find the area, or probability, in each region. a. T

Answer from: Quest

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Answer from: Quest

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step-by-step explanation:

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For a t distribution with 16 degrees of freedom, find the area, or probability, in each region. a. T...