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The problem asks to find the mean of \( D \), which is the difference between Andy's and Jim's times in the 100-meter dash, where \( D = A - J \). 

From the problem:
- \( \mu_A = 11.5 \) seconds (mean time for Andy),
- \( \mu_J = 10.5 \) seconds (mean time for Jim).

The formula for the mean of the difference of two random variables is:
\[
\mu_D = \mu_A - \mu_J
\]

Substituting the given values:
\[
\mu_D = 11.5 - 10.5 = 1.0 \text{ seconds}
\]

So, the mean of \( D \) is 1.0 seconds.

Do you want more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the variance of \( D \) be calculated?
2. How do independent random variables affect the computation of the variance of a difference?
3. What is the probability that Andy wins the race given the distribution of times?
4. If Andy's time variance increases, how does that affect the mean and variance of \( D \)?
5. How would a non-normal distribution of times for Andy or Jim change the calculation?

**Tip:** The mean of the sum or difference of two independent random variables is simply the sum or difference of their individual means.

Andy and Jim are going to compete in the 100-meter dash against each other. Let A be the time it takes Andy to complete the race, and J be the time it takes Jim to complete the race. Find the mean of D, the difference between their times (D = A - J), given μ_A = 11.5 seconds, σ_A = 1 second, μ_J = 10.5 seconds, and σ_J = 0.5 seconds.

Learn how to calculate the mean of the difference between two independent random variables, represented by the race times of Andy and Jim in a 100-meter dash. Given the means and standard deviations of both racers' times, we use the properties of expectation to solve for the mean of D.

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