I'm not sure what's the normal number, but there are currently over 200 hundred users with a reputation of 1 on MSE and some relatively active posts, of which over 20 users have a few posts with score higher than 5 and sometimes a very big absolute score.
See the query 1-reputation users with a meta posts with more than 5 votes, which currently finds:
scores User Link
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2900 Lightness Races BY-SA 3.0
2603 einpoklum
2385 ABANDON STACK -- Jeremy Banks
1768 Mari-Lou A
715 The forest of Reinstate Monica
270 Steven Penny
254 Madness - This is SE
216 peterh - Reinstate Monica
210 I am not the way you speak
201 Masked Man
150 Evan Carroll
94 Rounin
78 StackExchange for All
67 aloneprism
53 Maika Sakuranomiya
33 shiny-metal
32 Asadefa
31 Namaste
18 user311362
11 Sockenpuppe
8 What's in a Google Search
8 user361150
7 Vlad