Answer:a) P(x=r) = e^-4.3 × 4.3^r/(r!), b) 0.7637
Step-by-step explanation: The employee receives an average of 2.15 emails in one week.
This is the constant rate at which the event is occurring and it does not affect any other.
Hence λ = 2.15.
If she receives 2.15 emails in 1 week, then in 2 week, she will receive an average of 2.15×2 = 4.3.
Hence for the 2 week period, λ = 4.3 ( that's she receives and average of 4.3 emails in 2 weeks).
a) the probability distribution that defines a possion probability distribution is given below as
P(x=r) = e^-λ × λ^r/(r!)
Our question is to get the distribution, hence our answer will be in terms of r and λ= 4.3
P(x=r) = e^-4.3 × 4.3^r/(r!)
b) P(4 or fewer emails) = P(x≤4)
P(x≤4) = P(x=4) + P(x=3) + P(x=2) + P(x=1) +P(x=0)
Recall that
P(x=r) = e^-4.3 × 4.3^r/(r!)
At x = 4
P(x=4) = e^-4.3 × 4.3^4/(4!)
P(x=4) =e^-4.3 × 4.3^4/24
P(x=4) = 0.3866
At x = 3
P(x=3) = e^-4.3 × 4.3^3/(3!)
P(x=3) = e^-4.3 × 4.3^3/(6)
P(x=3) = 0.1798.
At x = 2
P(x=2) = e^-4.3 × 4.3^2/(2!)
P(x=2) = e^-4.3 × 4.3^2/(2)
P(x=2) = 0.1254
At x = 1
P(x=1) = e^-4.3 × 4.3^1/(1!)
P(x=1) = e^-4.3 × 4.3^1/(1)
P(x=1) = 0.0583
At x = 0
P(x=0) = e^-4.3 × 4.3^0/(0!)
P(x=0) = e^-4.3 × 1/(1)
P(x=0) = 0.0136
P(x≤4) = 0.3866+0.1798+0.1254+0.0583+0.0136 = 0.7637
