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For nearly two years, Minneapolis waited for answers about the fatal police shooting of Justine Ruszczyk, an unarmed woman who had called 911 seeking help. There was no video of the shooting. There was no audio. And the officer involved, Mohamed Noor, would not answer investigators’ questions.

But on Tuesday, after a monthlong trial in downtown Minneapolis, a jury handed down a verdict that is exceedingly rare in police shooting cases: Mr. Noor was guilty of murder.

The shooting of Ms. Ruszczyk, 40, set off outrage as far away as Australia, where she had lived for most of her life, and forced changes in the policies and leadership of the Minneapolis Police Department. The trial drew intense attention among Minnesota’s Somali-American residents, many of whom wondered whether Mr. Noor, who was born in Somalia, would be treated fairly.

No other Minnesota officer has been convicted in recent decades in a fatal on-duty shooting.

Jurors convicted Mr. Noor of third-degree murder, which carries a maximum sentence of 25 years in prison, and second-degree manslaughter, which can lead to as many as 10 years in prison. Under Minnesota sentencing guidelines, he will likely face several years in prison, but far fewer than the maximum.