Question

What is the probability that at most 5 defective fuses will be found in a box of 200 fuses, if 2% of such fuses are defective?

• A. 0.82
• B. 0.79
• C. 0.59
• D. 0.82

Answer 1

The correct option is B 0.79

The probability of finding defective fuses, p = 2/100.
Therefore average number of defective fuses in a box of 200 fuses $=np=200\times \frac{2}{100}=4.$

Therefore the mean of the Poisson distribution is given by $\lambda =4$

Required probability,

$P(r\le 5)={\sum }_{r=0}^5\frac{4^r{e}^{-4}}{r!}$

$=e^{-4}(1+4+\frac{4^2}{2!}+\frac{4^3}{3!}+\frac{4^4}{4!}+\frac{4^5}{5!})$

= 0.7845