Question

In her last ten 10K runs, Celia had the following times in minutes: 50:30, 50:37, 48:29, 50:46, 51:12, 49:19, 49:50, 51:19, 53:39, and 53:54
Based on these results, what is the best prediction of the number of times Celia will run faster than 50 minutes in her next 30 runs?

Answer 1

To estimate how many times Celia will run faster than 50 minutes in her next 30 runs based on her last ten 10K times, we start by determining how many of her past runs were faster than 50 minutes.

The times in minutes can be converted as follows:
- 50:30 → 50.5 minutes
- 50:37 → 50.617 minutes
- 48:29 → 48.483 minutes
- 50:46 → 50.767 minutes
- 51:12 → 51.2 minutes
- 49:19 → 49.317 minutes
- 49:50 → 49.833 minutes
- 51:19 → 51.317 minutes
- 53:39 → 53.65 minutes
- 53:54 → 53.9 minutes

Now, we identify which times are under 50 minutes:
- 48:29 (48.483)
- 49:19 (49.317)
- 49:50 (49.833)

Thus, out of the 10 runs, Celia ran faster than 50 minutes in **3 times**.

Next, to predict how many times she will run faster than 50 minutes in her next 30 races, we can calculate the proportion of times she has already run faster than 50 minutes:

\[
\text{Proportion of faster runs} = \frac{3}{10} = 0.3
\]

Now we multiply this proportion by 30 to find the expected number of runs faster than 50 minutes:

\[
\text{Expected number of faster runs in 30 races} = 0.3 \times 30 = 9
\]

So, based on her past performance, we can predict that **Celia will likely run faster than 50 minutes in approximately 9 of her next 30 runs**.