Stop and Wait Efficiency

A sender uses Stop and Wait protocol for transmission of 8000K bits size frames on a 1Gbps satellite channel with a propagation delay of $$400ms$$.What will be the link utilization(in percent),if probability of single frame error is 0.001.Assuming Ack from receiver have negligible transmission time.

My Work.

Though Stop and Wait has a window size of 1, I assume suppose I have 1000 frames to send.Now out of this 1 will be garbled(error rate is 0.001) and that would be retransmitted.

So, I calculated Link utilization as

$$\frac{useful\,time}{total\,time} \times 100$$

Now time to transmit 1 single 8000K bit frame over 1Gbps satellite channel would be $$8ms.$$

My Useful time would be $$1000 \times 8(ms)$$

Assuming $$T_{ack}=0$$, my total time for 1 frame would be $$8+800=808ms$$

So, my total time is $$1001 \times 808\, ms$$(1001 because 1 extra retransmission would be required).

So, efficiency=$$\frac{8 \times 1000}{1001 \times 808} \times 100=0.98 \%$$

Is my approach correct?