The scholars have differed in opinion over women reading silently and aloud in prayer. Their difference is based on whether they consider her voice an “awra” -parts not supposed to be exposed- or not. but the reason for this difference is whether she is present amongst strangers, if she is, she should conceal her voice, and if she is in the presence of her guardians-family- and women, then she may speak openly, and the details of the question are:

In the Kuwaiti Encyclopedia of Jurisprudence it says:

Majority of the Shafi’ and Hanbalis’ have said that if a woman is alone, or in the presence of women, or guardians she may recite louder and if she prays amongst strangers then she must conceal her voice.

Malikis have expressed dislike over women reading aloud in the prayer, and they explained that if she is amongst strangers who fear the loudness of her voice may cause temptation, then she should only be heard by herself.

And we take from the Hanafi scholars- supported by part the Shafi’s and the Hanbalis- is that the woman should always conceal her voice, 

Ibn Al Hamaam said: should there be an opinion that believes if she recites aloud in prayer, her salah becomes invalid, then this would be correct. and this is one of the two opinions attributed to the Shafi’s

An-Nawawi said: If she reads out loud where we recommended she reads silently, then her prayer is not invalidated. This is the correct opinion of the Shafis’ school. 

A summary of the sayings of the scholars on this issue:

If a woman is reciting out loud and a stranger heard her, then she should recite quietly in her prayer. This silent recitation is by reading in a way that will be loud enough that she can hear herself. However if she is with women or family members or guardians who are men, then she may recite out loud in the prayer.