There is a death in 1931 in Dumbarton for an Elizabeth Murray/Mcintosh born c. 1861 that you might consider viewing also to see who reported the death to try and confirm details.
From the birth cert you now have for the birth of Jean Murray in 1893, the address showed as 54 High Street Dumbarton. The 1891 census has this entry:
Lizzie Murray 29, rope worker
Mary Murray 8
Michael Murray 4
Address: 90 High Street, Dumbarton
Likely both Michael and Jane took on the McIntosh name after their mother's marriage to Robert McIntosh in 1895 (or at least son Michael also showed under McIntosh for that 1901 census entry we have).
There are two possible birth entries for an Elizabeth Murray showing on IGI in Dumbarton, in 1861 and 1862. The best place to confirm her entry and parents' details will be through her marriage and/or death cert which should include their full names.
Monica