A Quinnipiac University poll released this morning found that most New Yorkers do not think publishing executive Cathie Black is qualified to run the city’s school system. Her approval rating dropped further when voters with children in the public schools were polled.

Sixty-two percent of parents with children in the public school system disapprove of Mayor Bloomberg’s choice for the next chancellor and 63 percent say Black isn’t qualified. Fifty-one percent of voters in general think she’s not fit for the job.

A majority of voters, 64 percent, think that experience in education is important for whoever manages the city’s school system.

“Do New Yorkers approve of the Black appointment? Does she have the right experience? No and no, voters say,” said Quinnipiac pollster Mickey Carroll in a statement.

“The only positive sign for her is that about one quarter of voters don’t know enough to say whether they approve or disapprove of her appointment,” he said.

Asked about Chancellor Joel Klein’s tenure, 46 percent of voters said it has been a success. His approval ratings have varied over the years. When he took the position in 2003, 46 percent of voters approved of the job he was doing, but by March of 2007 that had dipped to about 33 percent. Last February, it was up to 39 percent.

Disappointment with Black’s nomination may have made its way into the mayor’s own approval ratings, which dropped to a level they hadn’t hit since 2005. Currently, 55 percent of voters think Mayor Bloomberg is doing a good job. Of those polled, 48 percent of voters disapprove of the way he’s running the public schools.