<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-06-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000728535</issuerCik>
        <issuerName>HUNT J B TRANSPORT SERVICES INC</issuerName>
        <issuerTradingSymbol>JBHT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001190258</rptOwnerCik>
            <rptOwnerName>THOMPSON JAMES K</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>615 J.B. HUNT CORPORATE DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LOWELL</rptOwnerCity>
            <rptOwnerState>AR</rptOwnerState>
            <rptOwnerZipCode>72745-</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and Chief Executive</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2004-06-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6600</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.5</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>221944</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2004-06-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3218</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.62</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>218726</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2004-06-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>8888</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.16</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>227614</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2004-06-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5360</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.62</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>222254</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2004-06-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>15000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>6.95</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>237254</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2004-06-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6842</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.62</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>230412</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2004-06-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.31</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>233412</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2004-06-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1267</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.62</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>232145</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-01</value>
            </transactionDate>
            <deemedExecutionDate>
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            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>8336</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>6</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>240481</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2004-06-01</value>
            </transactionDate>
            <deemedExecutionDate>
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            </deemedExecutionDate>
            <transactionCoding>
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                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3640</value>
                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>236841</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>6.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
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                </natureOfOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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                <value>Common Stock</value>
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            <transactionDate>
                <value>2004-06-01</value>
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            <transactionCoding>
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                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2712</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.62</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>240129</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
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        <nonDerivativeTransaction>
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            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7600</value>
                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                <natureOfOwnership>
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        <nonDerivativeTransaction>
            <securityTitle>
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            <deemedExecutionDate>
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            </transactionCoding>
            <transactionTimeliness>
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            <transactionAmounts>
                <transactionShares>
                    <value>3435</value>
                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
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            <transactionAmounts>
                <transactionShares>
                    <value>15000</value>
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                <transactionPricePerShare>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            </transactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
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            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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                <value>Common Stock</value>
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            <transactionDate>
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            </transactionDate>
            <deemedExecutionDate>
                <value>2004-06-01</value>
            </deemedExecutionDate>
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            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>24706</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.62</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>276690</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
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                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock 401(k)</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2880</value>
                </sharesOwnedFollowingTransaction>
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            <transactionCoding>
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                <value>Right to Buy   Stock Option</value>
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            <securityTitle>
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            <transactionDate>
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            <deemedExecutionDate>
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    <footnotes></footnotes>

    <ownerSignature>
        <signatureName>Debbie Willbanks</signatureName>
        <signatureDate>2004-06-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0202
4
2004-06-01
0
0000728535
HUNT J B TRANSPORT SERVICES INC
JBHT
0001190258
THOMPSON JAMES K
615 J.B. HUNT CORPORATE DRIVE
LOWELL
AR
72745-
1
1
0
0
President and Chief Executive
Common Stock
2004-06-01
2004-06-01
4
M
0
6600
8.5
A
221944
D
Common Stock
2004-06-01
2004-06-01
4
F
0
3218
33.62
D
218726
D
Common Stock
2004-06-01
2004-06-01
4
M
0
8888
14.16
A
227614
D
Common Stock
2004-06-01
2004-06-01
4
F
0
5360
33.62
D
222254
D
Common Stock
2004-06-01
2004-06-01
4
M
0
15000
6.95
A
237254
D
Common Stock
2004-06-01
2004-06-01
4
F
0
6842
33.62
D
230412
D
Common Stock
2004-06-01
2004-06-01
4
M
0
3000
5.31
A
233412
D
Common Stock
2004-06-01
2004-06-01
4
F
0
1267
33.62
D
232145
D
Common Stock
2004-06-01
2004-06-01
4
M
0
8336
6
A
240481
D
Common Stock
2004-06-01
2004-06-01
4
F
0
3640
33.62
D
236841
D
Common Stock
2004-06-01
2004-06-01
4
M
0
6000
6.75
A
242841
D
Common Stock
2004-06-01
2004-06-01
4
F
0
2712
33.62
D
240129
D
Common Stock
2004-06-01
2004-06-01
4
M
0
7600
6.75
A
247729
D
Common Stock
2004-06-01
2004-06-01
4
F
0
3435
33.62
D
244294
D
Common Stock
2004-06-01
2004-06-01
4
M
0
15000
10.4
A
259294
D
Common Stock
2004-06-01
2004-06-01
4
F
0
7898
33.62
D
251396
D
Common Stock
2004-06-01
2004-06-01
4
M
0
50000
8.81
A
301396
D
Common Stock
2004-06-01
2004-06-01
4
F
0
24706
33.62
D
276690
D
Common Stock 401(k)
2880
D
Stock Option
8.81
2004-06-01
2004-06-01
4
M
0
50000
8.81
D
1993-06-01
2006-11-02
Common Stock
50000
100000
D
Right to Buy   Stock Option
5.31
2004-06-01
2004-06-01
4
M
0
3000
5.31
D
2001-06-01
2006-10-12
Common Stock
3000
3000
D
Right to Buy   Stock Option
6
2004-06-01
2004-06-01
4
M
0
8336
6
D
2000-06-01
2007-01-25
Common Stock
8336
8334
D
Right to Buy   Stock Option
6.75
2004-06-01
2004-06-01
4
M
0
6000
6.75
D
2000-06-01
2005-11-05
Common Stock
6000
0
D
Right to Buy   Stock Option
6.75
2004-06-01
2004-06-01
4
M
0
7600
6.75
D
2000-06-01
2009-11-05
Common Stock
7600
38000
D
Right to Buy   Stock Option
6.95
2004-06-01
2004-06-01
4
M
0
15000
6.95
D
2002-06-01
2012-11-02
Common Stock
15000
105000
D
Right to Buy   Stock Option
8.5
2004-06-01
2004-06-01
4
M
0
6600
8.5
D
1995-06-01
2005-07-13
Common Stock
6600
0
D
Right to Buy   Stock Option
10.4
2004-06-01
2004-06-01
4
M
0
15000
10.4
D
1997-06-01
2007-07-18
Common Stock
15000
30000
D
Right to Buy   Stock Option
14.16
2004-06-01
2004-06-01
4
M
0
8888
14.16
D
2004-06-01
2013-10-24
Common Stock
8888
71112
D
Right to Buy   Stock Option
24.4
2009-06-01
2014-10-23
Common Stock
50000
50000
D
Debbie Willbanks
2004-06-03