You need to append " selected" to the option you want pre-selected in the dropdown.
<label for="day">Select Option:</label>
<select name="day">
<option value="0"<?php if ($query['day'] == 0) echo ' selected="selected"'; ?>>Monday</option>
<option value="1"<?php if ($query['day'] == 1) echo ' selected="selected"'; ?>>Tuesday</option>
<option value="2"<?php if ($query['day'] == 2) echo ' selected="selected"'; ?>>Wednesday </option>
<option value="3"<?php if ($query['day'] == 3) echo ' selected="selected"'; ?>>Thursday</option>
<option value="4"<?php if ($query['day'] == 4) echo ' selected="selected"'; ?>>Friday</option>
</select>