Question

use the aleks calculator to solve the following problems.
(a) consider a t distribution with 2 degrees of freedom. compute ( p(-1.93 < t < 1.93) ). round your answer to at least three decimal places.
( p(-1.93 < t < 1.93)=)
(b) consider a t distribution with 22 degrees of freedom. find the value of ( c ) such that ( p(t leq c)=0.10 ). round your answer to at least three decimal places.
( c=-1.321 )

Explanation:

Step1: Use the property of t - distribution

For a t - distribution, \(P(-a < t < a)=1 - 2P(t\geq a)\) when the degrees of freedom is \(df\). Here \(a = 1.93\) and \(df=2\).
First, find \(P(t\geq1.93)\) using the t - distribution table or calculator.

Step2: Calculate \(P(-1.93 < t < 1.93)\)

Using the formula \(P(-1.93 < t < 1.93)=1-2P(t\geq1.93)\).
When \(df = 2\), \(P(t\geq1.93)\approx0.107\) (using ALEKS calculator or t - table).
Then \(P(-1.93 < t < 1.93)=1 - 2\times0.107=1 - 0.214 = 0.786\)

Answer:

\(P(-1.93 < t < 1.93)=0.786\)