Alaska, Hawaii, Montana and Wyoming are not epicenters of the coronavirus pandemic. Yet these four states scored big this spring when Congress pumped out direct federal aid, while the two hardest-hit states, New York and New Jersey, got comparatively little given the vast numbers of cases and deaths they have seen.

An Associated Press analysis shows that some states with small populations like these took in an out-sized share of the $150 billion in federal money that was designed to address coronavirus-related expenses, when measured by the number of positive tests for the COVID-19 disease.

Their haul ranged from $2 million per positive test in Hawaii to nearly $3.4 million per test in Alaska. In Wyoming, with less than 600 positive cases, the $1.25 billion it received equates to 80 percent of its annual general state budget.

By comparison, New York and New Jersey received about $24,000 and $27,000, respectively, for each positive coronavirus test. Other states with high numbers of cases, including Massachusetts, Michigan and Illinois, received less than $100,000 per case.

“If there’s a fire, you don’t spray the whole neighborhood. You spray the house that’s on fire,” said Bill Hammond, director of public health policy at the Empire Center for Public Policy, a nonpartisan government watchdog in New York. He said it doesn’t make sense in this case to follow the normal political procedure of giving every state so much in the face of a public health crisis.

To be sure, the lowest population states often receive higher dollar amounts per capita when Congress doles out federal aid. That’s due in part to political reality: Small states have the same number of U.S. senators as more populous ones, and those senators lobby hard for their states’ interests.

The awards in the relief act passed in late March were based on population, but with a catch: Every state was to receive at least $1.25 billion, regardless of its size. Lawmakers said setting such a minimum was needed to reach a deal in a divided government.

In the coronavirus fight, the disproportionate share going to smaller states has consequences. States with high numbers of infections and deaths say they need that money for immediate expenses related to fighting an outbreak that threatened to overwhelm their hospital systems, from staff overtime to setting up makeshift hospitals.

The money for state governments is a slice of a $2.2 trillion federal stimulus. Governments are supposed to use it for new coronavirus expenses incurred from March 1 through Dec. 30. Under federal guidelines, the money cannot be used for other purposes, like making up for lost tax revenue to keep general government services running.

Some states with relatively few cases have been able to reopen their economies faster and have more options on how to spend the federal largess. Many are now trying to determine how they can spend the windfall while keeping within the federal guidelines.

Wyoming Gov. Mark Gordon, a Republican, is proposing using a portion of the money to help businesses that have suffered because of government-imposed shutdowns and shrunken demand, even though other parts of the federal aid are already aimed at businesses.

Gordon noted neighboring Idaho — which received more than $600,000 per positive test — already has a similar system in place. In a public meeting streamed on video, Gordon said he knew the state would be watched carefully. After all, the state’s allocation is five times per capita what New York received and nearly 90 times as much per positive coronavirus test.