The $3,000 loss will still carry over as it is report on line 13 of a Form 1040 and your Standard deduction is on line 40 they are two completely separate items and have no bearing on each other.
A standard deduction is based on your filing status wheras the investment loss carryover is based on a prior year tax return so, you can tax both. Now, if you Itemize (Schedule A) then you can only take either itemized deductions or standard deduction, but not both.
There is also an exemption which is on line 42 which can further decrease the income subject to income tax.
