The Jewish Nation - For Men Only

In preparation for the revelation at Sinai, Moses tells the people not to go near (i.e., have relations with) women for three days. It is therefore obvious from the context that the people, הָעָם, the nation, excludes women. Does this suggest that when הָעָם is used in the passages immediately adjacent to v. 15, that women are also excluded? Did the women not prepare and wash their garments (v. 14)? Did only the men shudder (v. 16)? Did only the men stand at the foot of the mountain (v. 17)? Etcetera.

14. So Moses descended from the mountain to the people, and he prepared the people, and they washed their garments.		יד. וַיֵּרֶד מֹשֶׁה מִן הָהָר אֶל הָעָם וַיְקַדֵּשׁ אֶת הָעָם וַיְכַבְּסוּ שִׂמְלֹתָם:
15. He said to the people, "Be ready for three days; do not go near a woman."		טו. וַיֹּאמֶר אֶל הָעָם הֱיוּ נְכֹנִים לִשְׁלֹשֶׁת יָמִים אַל תִּגְּשׁוּ אֶל אִשָּׁה:
16. It came to pass on the third day when it was morning, that there were thunder claps and lightning flashes, and a thick cloud was upon the mountain, and a very powerful blast of a shofar, and the entire nation that was in the camp shuddered.		טז. וַיְהִי בַיּוֹם הַשְּׁלִישִׁי בִּהְיֹת הַבֹּקֶר וַיְהִי קֹלֹת וּבְרָקִים וְעָנָן כָּבֵד עַל הָהָר וְקֹל שֹׁפָר חָזָק מְאֹד וַיֶּחֱרַד כָּל הָעָם אֲשֶׁר בַּמַּחֲנֶה:
17. Moses brought the people out toward God from the camp, and they stood at the bottom of the mountain.		יז. וַיּוֹצֵא מֹשֶׁה אֶת הָעָם לִקְרַאת הָאֱ־לֹהִים מִן הַמַּחֲנֶה וַיִּתְיַצְּבוּ בְּתַחְתִּית הָהָר:

I could not find any meforshim that discuss this problem. Is there no commentator that is troubled by the exclusionary wording of Exodus 19:15?