According to the poll, 47 percent of those questioned support Dole while 40 percent plan to vote for Bowles. Thirteen percent were undecided.
Libertarian Sean Haugh, the only other candidate to appear on the ballot, was not included in the poll because he did not participate in either of two televised debates and did not campaign actively across the state.
In a press release, UNC journalism Professor Robert Stevenson, the poll's director, said if undecided voters select between the two candidates in the same proportions as decided voters, the likely Dole margin is 8 percentage points.
The poll results come from interviews with a representative sample of 560 registered voters statewide in the week ending Thursday.
According to the poll, support for Bowles is especially strong among young voters and blacks, while Dole is popular with men. It also showed candidate preference is spread evenly across the state. A random sample of this size has a maximum error of about 5 percent.
The poll, in its 20th year, is carried out by journalism students under faculty supervision.
Though poll results are generally accurate, it must be taken into consideration that some people change their minds before the election, said UNC political science Professor Thad Beyle.
He said issues that were bothering a person can manifest themselves in the last days of a campaign. "When there's movement going on, you can be somewhat surprised," he said. "People are making up their minds at the last minute."
Dole will continue her grass-roots campaign in the last days of her campaign, said Dole spokeswoman Janet Bradbury. She said Dole will not increase her actions to maintain her lead.