The correct way would be: While she was sleeping, the alarm kept ringing in Jamie's ear.
<u><em>While</em></u> contains the element of duration and it is better to use a progressive form.
<u><em>Sleeping</em></u><em> </em>is a verb that has duration, so it should not be conjugated in the past simple if there is a simultaneous action.
Some of the exports of Brazil are soybeans, sugar, orange juice and iron ore.
(If you need a definition why, let me know)
By Giving Her Seat To the fellow passenger
Love makes time go by faster.