Questions: Consider a t distribution with 10 degrees of freedom. Compute P(t ≥ -1.73). Round your answer to at least three decimal places.
P(t ≥ -1.73)=
Transcript text: Consider a $t$ distribution with 10 degrees of freedom. Compute $P(t \geq-1.73)$. Round your answer to at least three decimal places.
\[
P(t \geq-1.73)=
\]
Solution
Solution Steps
To solve this problem, we need to calculate the probability that a t-distributed random variable with 10 degrees of freedom is greater than or equal to -1.73. This can be done using the cumulative distribution function (CDF) of the t-distribution. Since the CDF gives the probability that a random variable is less than or equal to a certain value, we can use it to find the probability of being greater than or equal to -1.73 by subtracting the CDF value from 1.
Step 1: Define the Problem
We need to compute the probability P(t≥−1.73) for a t-distribution with 10 degrees of freedom.
Step 2: Use the CDF of the t-Distribution
The cumulative distribution function (CDF) for the t-distribution gives us the probability that a random variable t is less than or equal to a certain value. Therefore, we can express the desired probability as:
P(t≥−1.73)=1−P(t<−1.73)=1−F(−1.73)
where F(−1.73) is the CDF evaluated at −1.73.
Step 3: Calculate the Probability
Using the CDF for a t-distribution with 10 degrees of freedom, we find:
F(−1.73)≈0.057158
Thus, we can calculate:
P(t≥−1.73)=1−0.057158≈0.942842
Step 4: Round the Result
Rounding the result to three decimal places, we have:
P(t≥−1.73)≈0.943