Question

use the aleks calculator to solve the following problems.
(a) consider a t distribution with 9 degrees of freedom. compute ( p(tgeq1.39) ). round your answer to at least three decimal places.
( p(tgeq1.39)=square )
(b) consider a t distribution with 29 degrees of freedom. find the value of ( c ) such that ( p(-clt tlt c)=0.99 ). round your answer to at least three decimal places.
( c=square )

Explanation:

Step1: Compute \(P(t\geq1.39)\) for \(t\) - distribution with \(9\) degrees of freedom

Using the ALEKS calculator (or a \(t\) - distribution table/software), for a \(t\) - distribution with \(n = 9\) degrees of freedom, we find the right - tailed probability.
The formula for the right - tailed probability of a \(t\) - distribution \(P(T\geq t)\) where \(T\sim t(n)\) is calculated directly.
When \(n = 9\) and \(t = 1.39\), \(P(t\geq1.39)\approx0.095\)

Step2: Find \(c\) for \(P(-c < t < c)=0.99\) with \(29\) degrees of freedom

Since the \(t\) - distribution is symmetric about \(0\), \(P(-c < t < c)=1 - 2P(t\geq c)\).
We know that \(1 - 2P(t\geq c)=0.99\), then \(2P(t\geq c)=1 - 0.99=0.01\), and \(P(t\geq c)=\frac{0.01}{2}=0.005\)
Using the ALEKS calculator (or a \(t\) - distribution table/software) with \(n = 29\) degrees of freedom, we look for the \(t\) - value \(c\) such that the right - tailed probability \(P(t\geq c)=0.005\).
The value of \(c\approx2.756\)

Answer:

a. \(P(t\geq1.39)=0.095\)
b. \(c = 2.756\)