A headphone manufacturer guarantees that the company will repair any headphone that is defective within one year warranty period for free. Past records showed that 5% of their headphone needed repair during the warranty period. The company sold 30 headphones last January. If the average cost of repairing a headphone is 70$, calculate the expected cost the manufacturer needs to bear in repairing not more than four headphones.
Can anyone help me with this question because i'm confused if i need to use approximation or not. Thank your for your help :)
Hint:
The expected cost are $\mathbb E(C)=70\cdot \sum\limits_{k=0}^4 P(X=k)\cdot k$, where $X\sim Bin(30, 0.05)$ and $k$ are the number of headphones need to be repaired.