Question

If jobs arrive every 15 seconds on average, what is the probability of waiting more than 30 seconds?

Answer 1

Answer: 0.14

Step-by-step explanation:

Given: Mean : $\lambda=15\text{ per seconds}$

In minutes , Mean : $\lambda=4\text{ per minute}$

The exponential distribution function with parameter $\lambda$  is given by :-

$f(t)=\lambda e^{-\lambda t}, \text{ for }x\geq0$

The probability of waiting more than 30 seconds i.e. 0.5 minutes is given by the exponential function :-

$P(X\geq0.5)=1-P(X\leq0.5)\\\\=1-\int^{0.5}_{0}4e^{-4t}dt\\\\=1-[-e^{-4t}]^{0.5}_{0}\\\\=1-(1-e^{-2})=1-0.86=0.14$

Hence, the probability of waiting more than 30 seconds = 0.14