`lifeexpectancy` values are per-country. You need to decide whether you want the region averages to accurately represent regions by being weighted by country population, or just the relatively meaningless arithmetic average per-country regardless of population. I'll assume you want the more accurate weighted average.
-- make region populations easily available
create or replace view regionpops as
select region, sum(population) as regionpop
from country
group by region;
-- regional average life expectancies
select region, sum( a.lifeexpectancy * a.population / b.regionpop )
from country a
join regionpops b using(region)
group by region;
Now that query becomes the subquery for your answer. Here I added the lifeexpectancy values to the Select list as a check on the calculation making sense:
select region, sum(population) as popsum, a.lifeexpectancy, b.regionLE
from country a
join (
select region, sum( a.lifeexpectancy * a.population / b.regionpop ) as regionLE
from country a
join regionpops b using(region)
group by region
) b using(region)
where a.lifeexpectancy < b.regionLE
group by region;
+---------------------------+------------+----------------+----------+
| region | popsum | lifeexpectancy | regionLE |
+---------------------------+------------+----------------+----------+
| Baltic Countries | 2424200 | 68.4 | 68.82284 |
| British Islands | 3775100 | 76.8 | 77.64641 |
| Caribbean | 8316000 | 64.5 | 69.21611 |
| Central Africa | 19436000 | 38.3 | 48.08958 |
| Central America | 29461000 | 70.9 | 70.99977 |
| Eastern Africa | 47507000 | 37.6 | 45.18690 |
| Eastern Asia | 1304259000 | 71.4 | 72.30971 |
| Eastern Europe | 35026400 | 70.9 | 71.42139 |
| Melanesia | 4807000 | 63.1 | 64.34627 |
| Micronesia | 297000 | 59.8 | 70.55470 |
| Middle East | 57449000 | 66.4 | 67.15592 |
| Nordic Countries | 4521500 | 78.4 | 79.27854 |
| North America | 128000 | 76.9 | 79.37417 |
| Northern Africa | 68763000 | 63.3 | 66.50646 |
| Polynesia | 200000 | 71.1 | 72.39442 |
| South America | 179305000 | 63.7 | 67.03645 |
| Southeast Asia | 63097000 | 46.0 | 65.85890 |
| Southern Africa | 3348000 | 39.3 | 50.34519 |
| Southern and Central Asia | 334412000 | 45.9 | 62.13517 |
| Southern Europe | 34507800 | 71.6 | 77.55884 |
| Western Africa | 63427000 | 50.2 | 50.35628 |
| Western Europe | 100931200 | 77.8 | 77.98879 |
+---------------------------+------------+----------------+----------+