Designing a common-emitter amplifier circuit
As its most likely a homework/class problem I'll take you through the process and let you finish it off.

For a silicon transistor the base voltage (Vb) will be about 0.6V higher than the emitter so if you know (or set) Ve you can write down Vb.

The gain of a small signal transistor will be at least 100 so if we take the current flowing through R1 and R2 as about 1/10th the collector (or emitter) current, When the potential divider (R1,R2) is connected to the transistor base the current taken by the base, Ib, will not significantly affect the 'calculated' voltage at the junction. By your calculation this will be about 0.1mA.

You can use Ohm's law to calculate the total resistance of R1 and R2  (= Vcc / 0.1mA = 15 * 10^3/ 0.1) = 150000 or 150k

Last part of the puzzle   R2/(R1+R2) * 15 = 1.6  (voltage divider equation)

As you already know (R1+R2 = 150k) the only unknown is R2

Once you calculate R2 then R1 is easy to find.

Finally, you should check your answers for nearest preferred values (say E24 series ). Instead of 0.995k use a 1k0 (npv).