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)=

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.

We need to compute the probability \( P(t \geq -1.73) \) for a t-distribution with 10 degrees of freedom.

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: \[ P(t \geq -1.73) = 1 - P(t < -1.73) = 1 - F(-1.73) \] where \( F(-1.73) \) is the CDF evaluated at \( -1.73 \).

Using the CDF for a t-distribution with 10 degrees of freedom, we find: \[ F(-1.73) \approx 0.057158 \] Thus, we can calculate: \[ P(t \geq -1.73) = 1 - 0.057158 \approx 0.942842 \]

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

Final Answer