Question

At a certain fire station, false alarms are received at a mean rate of .2 per day. In a year, what is the probability that fewer than 60 false alarms are received?

Answer 1

0.064

Explanation:

Number of days in a year = 365

Mean rate of false alarm in a year = λ = 365 * 0.2 = 73

Standard deviation, σ = sqrt(λ) = sqrt(73) = 8.54 (for large λ value)

Using the relation :

P(x < 60): (60 - 73) / 8.54

P(x < 60) = - 1.52

P(Z < - 1.52) = 0.06426 (Z probability calculator

= 0.064