Your date of death is correct per the SS record.
You will be able to obtain a copy of the death certificate for about $25.

First Name: Ida
Middle Name:
Last Name: Windnagle
Name Suffix:
Birth Date: 21 February 1893
Social Security Number: 366-68-7882
Place of Issuance: Michigan
Last Residence: Wayne, Michigan
Zip Code of Last Residence: 48224
Death Date: August 1972
Estimated Age at Death: 79

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First Name: Melvern
Middle Name:
Last Name: Windnagle
Name Suffix:
Birth Date: 26 October 1896
Social Security Number: 377-38-1149
Place of Issuance: Michigan
Last Residence: Wayne, Michigan
Zip Code of Last Residence: 48224
Death Date: September 1973
Estimated Age at Death: 77
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1930 census
Name: Melvern E Windnagle
Event: Census
Event Date: 1930
Event Place: Detroit (Districts 0751-0879), Wayne, Michigan
Gender: Male
Age: 33
Marital Status: Married
Race: White
Birthplace: Ohio
Estimated Birth Year: 1897
Immigration Year:
Relationship to Head of Household: Head
Father's Birthplace: Ohio
Mother's Birthplace: Ohio
Enumeration District Number: 0818
Family Number: 8
Sheet Number and Letter: 89B
Line Number: 75
NARA Publication: T626, roll 1065
Film Number: 2340800
Digital Folder Number: 4609305
Image Number: 00184
Household Gender Age Birthplace
Head Melvern E Windnagle M 33 Ohio
Wife Ida P Windnagle F 36 Ohio
Mother-in-law Ernestine Lorenz F 71 Germany
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WWII Draft Registration
Name: Melvern Earl Windnagle
Event: Draft Registration
Event Date: 1942
Event Place: Detroit, Wayne, Michigan
Gender: Male
Birth Date: 26 Oct 1896
NARA Publication Title: World War II Draft Cards (4th Registration) for the State of Michigan