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)=

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. \[ P(t \geq-1.73)= \]
failed

Solution

failed
failed

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(t1.73) P(t \geq -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 t is less than or equal to a certain value. Therefore, we can express the desired probability as: P(t1.73)=1P(t<1.73)=1F(1.73) P(t \geq -1.73) = 1 - P(t < -1.73) = 1 - F(-1.73) where F(1.73) F(-1.73) is the CDF evaluated at 1.73 -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 F(-1.73) \approx 0.057158 Thus, we can calculate: P(t1.73)=10.0571580.942842 P(t \geq -1.73) = 1 - 0.057158 \approx 0.942842

Step 4: Round the Result

Rounding the result to three decimal places, we have: P(t1.73)0.943 P(t \geq -1.73) \approx 0.943

Final Answer

0.943\boxed{0.943}

Was this solution helpful?
failed
Unhelpful
failed
Helpful