Aims: We analyzed the resolved stellar population of the C component of the extremely metal-poor dwarf galaxy I Zw18 in order to evaluate its distance and star formation history as accurately as possible. In particular, we aimed at answering the question of whether this stellar population is young. Methods: We developed a probabilistic approach to analyzing high-quality photometric data obtained with the Advanced Camera for Surveys of the Hubble Space Telescope. This approach gives a detailed account of the various stochastic aspects of star formation. We carried out two successive models of the stellar population of interest, paying attention to how our assumptions could affect the results. Results: We found a distance to the C component of I Zw 18 as high as 27 Mpc, a significantly higher value than those cited in previous works. The star formation history we inferred from the observational data shows various interesting features: a strong starburst that lasted for about 15 Myr, a more moderate one that occurred ≈100 Myr ago, a continuous process of star formation between both starbursts, and a possible episode of low level star formation at ages over 100 Myr. The stellar population studied is likely ≈125 Myr old, although ages of a few Gyr cannot be ruled out. Furthermore, nearly all the stars were formed in the last few hundreds of Myr.