Answer: the probability that there are three or fewer calls in one hour is 0.011
Step-by-step explanation:
The formula for poisson distribution is expressed as
P(x = r) = (e^- µ × µ^r)/r!
Where
µ represents the mean of the theoretical distribution.
r represents the number of successes of the event.
From the information given,
µ = 10
For the probability that there are three or fewer calls in one hour, it is expressed as
P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
Therefore,
P(x = 0) = (e^- 10 × 10^0)/0! = 0.000045
P(x = 1) = (e^- 10 × 10^1)/1! = 0.00045
P(x = 2) = (e^- 10 × 10^2)/2! = 0.0023
P(x = 3) = (e^- 10 × 10^3)/3! = 0.0077
Therefore,
P(x ≤ 3) = 0.000045 + 0.00045 + 0.0023 + 0.0077 = 0.011
