Question

If 2% electric bulbs manufactured by a company are defective, the probability that in a sample of 100 bulbs, exactly 5 are defective is -

• A. 4/15e²
• B. 5/16e²
• C. 3/8e²
• D. 1/15e²

Answer 1

Answer: (A)

4/15e²

Answer 2

Here p = $\frac { 2 } { 100 }$ = 0.02, n = 100, As n is large and p is small, we use Poisson approximation to binomial. We have l = np = 2 Let X = number of defective bulbs,

Then P(X = 5) = e^–l . $\frac { \lambda ^ { 5 } } { 5 ! }$ = e^–2 $\left( \frac { 2 ^ { 5 } } { 120 } \right)$ =$\frac { 4 } { 15 \mathrm { e } ^ { 2 } }$.