Question

use the aleks calculator to solve the following problems.
(a) consider a t distribution with 23 degrees of freedom. compute ( p(-1.84 < t < 1.84) ). round your answer
to at least three decimal places.
( p(-1.84 < t < 1.84)=square )
(b) consider a t distribution with 14 degrees of freedom. find the value of ( c ) such that ( p(t leq c)=0.05 ). round
your answer to at least three decimal places.
( c=-1.761 )

Explanation:

Step1: Use the property of t - distribution symmetry

For a t - distribution with \(n = 23\) degrees of freedom, \(P(-1.84\lt t\lt1.84)=1 - 2P(t\geq1.84)\)

Step2: Use the ALEKS calculator

Input the degree of freedom \(df = 23\) and the value \(x = 1.84\) into the ALEKS calculator's t - distribution function.
We find that \(P(t\geq1.84)\approx0.039\)
Then \(P(-1.84\lt t\lt1.84)=1-2\times0.039 = 0.922\)

Answer:

\(P(-1.84\lt t\lt1.84)=0.922\)