Answer
See answer.
Work Step by Step
The relationship between the sun's period T, mean distance r, and the galaxy’s mass M is derived in Example 5-14.
$$M=\frac{4 \pi ^2 r^3}{GT^2}$$
Substitute the values given to get the mass of the galaxy.
$$M=\frac{4 \pi ^2 (30000*9.5\times10^{15}m)^3}{G(200\times10^6 y*3.15\times10^7 s/y)^2}\approx3\times10^{41}kg$$
Dividing that mass by the mass of our sun, there would be about $2\times10^{11}$ stars in the galaxy.