Initiative 1098, a plan by Bill Gates Sr. and others to authorize an income tax on the wealthy and reduce some other taxes, is headed to the statewide ballot in Washington.

Although state officials are investigating apparent fraud by one of the campaign’s signature gatherers, the  state Elections Division announced late Thursday that a 3 percent random check of the huge number of unchallenged signatures showed easily enough valid signatures to assure a spot on the ballot.

The campaign had turned in about 385,000 signatures and 11,786 were reviewed, with 10,090 accepted. The others were turned down because no registration could be found for the signer, the signature didn’t match the one on file or there was no usable image on file for the signer, or because they were duplicates.  (The fraud investigation involves about 350 signatures on 20 petition sheets.)

It is the third voter initiative to be cleared for a statewide vote, and three more await signature checks.

On Tuesday, Reed certified I-1082, the plan to allow private insurers to offer coverage for workplace injuries. Currently the state runs the main program, although some large companies are allowed to self-insure.  The plan is backed by the Building Industry Association of Washington, and opposition also has formed.

On Monday, Secretary Reed certified I-1100, which would end the state liquor monopoly and allow current retailers to sell hard liquor along with their beer and wine.

Next up for a signature check is I-1053, Tim Eyman’s proposal to re-establish the two-thirds vote requirement for the state Legislature to raises taxes.  It turned in about 338,000 signatures.

After that: I-1105. This is a rival liquor initiative, supported by wholesalers, to take the state out of the liquor retail business. Whereas I-1100 would let retailers buy liquor stock directly from manufacturers, I-1105 would require use of wholesalers.

The last check will be I-1107. This measure would repeal new taxes on candy, pop, beer and bottled water. Backed by the American Beverage Association, it brought in 395,000 signatures in only three weeks.

The Legislature has sent three other measures to the statewide ballot this fall:

* Referendum  52 would authorize bonds to finance construction and repair projects increasing energy efficiency in public schools and higher education buildings, and continue the sales tax on bottled water otherwise expiring in 2013.

* House Joint Resolution 4220, known as the “Lakewood Police Officers Memorial Act,” would amend the state constitution on bail requirements for judges.

* Senate Joint Resolution 8225 would amend the state constitution relating to debt limits for the state.