A majority of the Supreme Court seemed ready on Monday to find that Florida has made it too hard to prove that a death row inmate is mentally retarded and thus ineligible for execution.

The decision, when it comes, could have consequences for a handful of states, including Virginia, that draw a rigid line on IQ-test results. Under their laws, an inmate who scores above 70 on the test cannot be considered intellectually disabled.

Several justices said that standard does not take into account the margin of error that professionals say is inherent in IQ tests. The justices questioned whether Florida simply intended to make more inmates eligible for the death penalty rather than truly sorting out which ones are mentally retarded.

Justice Anthony M. Kennedy, whose vote will probably be the most influential on the question, repeatedly questioned why the state adopted a hard cutoff for IQ scores when those who design such tests say there can be a five-point margin of error.

“Your rule prevents us from getting a better understanding of whether that IQ score is accurate or not,” Kennedy said.

Justice Elena Kagan had prompted Kennedy’s question by pressing Florida Solicitor General Allen Winsor about why the state wanted to set a rigid standard that precluded any other way of determining whether someone is mentally retarded.

“We have this whole line of cases that says when it comes to meting out the death penalty, we actually do individualized consideration, and we allow people to make their best case about why they’re not eligible for the death penalty,” Kagan said. “And essentially what your cutoff does is it stops that in its tracks.”

It was the court’s first consideration of state laws defining mental retardation in capital cases since its 2002 decision that executing the mentally retarded violated the Constitution’s prohibition against cruel and unusual punishment.

The hearing came on a snowy day in Washington when the rest of the federal government had shut down. And it came amid heightened security at the court after a group posted online footage of Supreme Court hearings that had been surreptitiously recorded by an audience member.

Security officers brought in bright lights to search through the personal items spectators took into the courtroom. (Cameras are not allowed in the courtroom, and any electronic device is forbidden.) More-sensitive metal detectors resulted in more people being pulled aside to take off belts or remove wallets for examination.

The case involved Freddie Lee Hall, 68, who has lived more than half his life on Florida’s death row. He was given the death penalty for raping and killing Karol Hurst, 21 years old and pregnant, after he and a co-defendant kidnapped her as she left a grocery store in 1978.

The men later that day killed a police officer who interrupted their plans to rob a convenience store.

Lawyers for Hall have argued in decades of court procedures that he should be spared because of a brutal childhood and because he has been identified since he was a boy, and later by some judges, as mentally retarded.

But for a person to be defined as mentally retarded in Florida, state law requires a showing of below-average intellectual functioning, along with deficits in “adaptive behavior” and proof that the onset of the intellectual disabilities began before age 18.

The first prong of that inquiry is the IQ-test score. The cutoff traditionally has been set at 70, Washington lawyer Seth Waxman told the court, because that is two standard deviations from the mean score of 100.

But he said margins of error must be taken into account, and Florida’s law doesn’t allow that. He cited opinions from the American Association on Intellectual and Developmental Disabilities and the American Psychiatric Association.

Justices Antonin Scalia and Samuel A. Alito Jr. were Waxman’s toughest questioners. Scalia noted that the court’s 2002 decision left it up to the states to define mental retardation and was not swayed by the opinions of the psychiatric associations.

“This APA is the same organization that once said that homosexuality was a mental disability and now says it’s perfectly normal,” Scalia said. “They change their minds.”

Winsor said that Hall has consistently scored above the 70 threshold in IQ tests administered over the years — “71, 72, 73, 74 and 80” — and that the court should defer to the judgment of the Florida legislature and courts.

Justice Stephen G. Breyer brought up the idea of having an expert testify in borderline cases that the tests have some imprecision. “What’s wrong with that?  It doesn’t sound so terrible.”

Another sign of trouble for Florida was Kennedy’s concern about the state’s administration of the death penalty. Although it was not pertinent to Hall’s argument, Kennedy said that “the last 10 people Florida has executed have spent an average of 24.9 years on death row.”

He asked Winsor: “Do you think that that is consistent with the purposes of the death penalty, and is it consistent with sound administration of the justice system?”

Winsor seemed surprised by the question but said attempts by the state to streamline the process are under legal attack.

Scalia jumped in to help. “General Winsor, maybe you should ask us that question, inasmuch as most of the delay has been because of rules that we have imposed,” he said.

The case is Hall v. Florida.