“Whether they robbed a store, pushed a man or whatever the case may be, there are other strategies and tactics the police officer should use before excessive force and brutally killing someone in cold blood,” Felicia Irving, 28, a high-school English teacher in Hampton, Ga., who is black, said in a follow-up interview.

Jean Smith, 75, a retiree in Hartford, Ala., who is white, said she could not determine “with just two or three facts” whether the officer, Darren Wilson, had been justified in shooting and killing Mr. Brown. “To know whether it was justified, I’d have to know the whole thing from beginning to end and look at it as objectively as possible,” Ms. Smith said.

The poll also shows significant differences in how blacks and whites view the unrest that has gripped Ferguson since Mr. Brown’s killing. Most whites say they think the actions of the protesters have gone too far, while blacks are more evenly divided. Thirty-eight percent of blacks think the protesters’ actions have been about right, compared with 15 percent of whites. A vast majority of the protesters in Ferguson have been black.