Answer:
Step-by-step explanation:
We would apply the formula for poisson distribution which 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 = 3.5
a)
For the probability that there will be at least 2 such accidents in the next month, it is expressed as
P(x ≥ 2) = 1 - P(x < 2)
P(x < 2) = P(x = 0) + P(x = 1)
Therefore,
P(x = 0) = (e^- 3.5 × 3.5^0)/0!
P(x = 0) = (e^- 3.5 × 1)/1
P(x = 0) = 0.03
P(x = 1) = (e^- 3.5 × 3.5^1)/1!
P(x = 1) = (e^- 3.5 × 3.5)/1
P(x = 1) = 0.11
P(x < 2) = P(x = 0) + P(x = 1) = 0.03 + 0.11 = 0.14
P(x ≥ 2) = 1 - 0.14 = 0.86
b)
For the probability that there will be at most 1 accident in the next month, it is expressed as
P(x ≤ 1) = P(x = 0) + P(x = 1)
P(x = 0) = 0.03
P(x = 1) = 0.11
P(x ≤ 1) = 0.03 + 0.11 = 0.14
