Roller Bearing

Consider a roller bearing is selected for a unique assembly. If the design requires a minimum basic load rating of 5.5 N and a design life of 10, what is the design radial load?

Hint
The minimum required basic load rating (the load in which 90% of bearings from a given lot will survive 1 million revolutions) is:
$$$C=PL^{1/a}$$$
where $$C$$ is the minimum required basic load rating, $$P$$ is the design radial load, $$L$$ is the design life (in millions of revolutions), and $$a$$ is the bearing coefficient.
Hint 2
For ball bearings: $$a=3$$
For roller bearings: $$a=\frac{10}{3}$$
The minimum required basic load rating (the load in which 90% of bearings from a given lot will survive 1 million revolutions) is:
$$$C=PL^{1/a}$$$
where $$C$$ is the minimum required basic load rating, $$P$$ is the design radial load, $$L$$ is the design life (in millions of revolutions), and $$a$$ is the bearing coefficient. For ball bearings, $$a=3$$ . However, the problem statement is asking for a roller bearing, so $$a=10/3$$ . Thus,
$$$5.5N=P(10\cdot 10^6)^{1/(10/3)}$$$
$$$P=\frac{5.5N}{10,000,000^{3/10}}=\frac{5.5N}{125.89}=0.04\:N$$$
0.4 N