Adding A Y/N Column Based On Criteria

Currently I'm trying to add a column based on certain criteria based on the following data:

CallID GroupName CustomerPending
------ ----------- ------------
00500588FollowupN
00500588FollowupN
00500588Server N
00500588Service DeskN
00500588Service DeskN

Basically I'm trying to add an extra column, so that whenever the GroupName is "Followup", then a 'Y' will appear in the CustomerPending column for all instances of that CallID. I tried with the following, but it only provides a 'Y' in the rows (not the CallId's) where "Followup" is found.

--------------------------------------
UPDATE dbo.Asgnmnt
SET CustomerPending = 'Y'
FROM dbo.Asgnmnt
WHERE dbo.Asgnmnt.GroupName IN ('SD Followup')

ALTER Table Asgnmnt
ALTER column CustomerPending varchar(1)

UPDATE dbo.Asgnmnt
SET CustomerPending = 'N'
FROM dbo.Asgnmnt
WHERE dbo.Asgnmnt.GroupName NOT IN ('SD Followup')

ALTER Table Asgnmnt
ALTER column CustomerPending varchar(1)
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Any assistance appreciated.