Question

use the aleks calculator to solve the following problems.
(a) consider a t distribution with 20 degrees of freedom. compute ( p(-1.95 < t < 1.95) ). round your answer to at least three decimal places.
( p(-1.95 < t < 1.95)=square )
(b) consider a t distribution with 27 degrees of freedom. find the value of ( c ) such that ( p(t geq c)=0.10 ). round your answer to at least three decimal places.
( c=1.314 )

Explanation:

Step1: Use the property of t - distribution

For a t - distribution, \(P(-a < t < a)=1 - 2P(t\geq a)\)

Step2: Find \(P(t\geq1.95)\) with 20 degrees of freedom

Using the ALEKS calculator (or t - table), for \(t\) - distribution with \(n = 20\) degrees of freedom, \(P(t\geq1.95)\) is found.

Step3: Calculate \(P(-1.95 < t < 1.95)\)

\(P(-1.95 < t < 1.95)=1-2P(t\geq1.95)\)
\(P(t\geq1.95)\approx0.032\) (using ALEKS calculator)
\(P(-1.95 < t < 1.95)=1 - 2\times0.032=1 - 0.064 = 0.936\)

Answer:

\(P(-1.95 < t < 1.95)=0.936\)