Between 3 p.m. and 5 p.m. the average number of phone calls per minute coming into the helpline desk of a bank is 5. The probability that during one particular minute there will be only one phone call is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(5e^{-5}\)
The number of calls in a minute follows a Poisson distribution with mean \(\lambda = 5\):
\( \displaystyle P(X = r) = \frac{e^{-\lambda}\lambda^r}{r!} \)
For exactly one call, r = 1:
\( \displaystyle P(X = 1) = \frac{e^{-5} \times 5^1}{1!} = 5e^{-5} \)