According to email logs, one employee at your company receives an average of 2.15 emails per week. Suppose the count of emails received can be adequately modeled as a Poisson random variable.

a. What is the distribution of the number of emails in a two-week period?
b. What is the probability of receiving 4 or fewer emails in a two-week period?

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

answer: 457.14

step-by-step explanation:

205 - 45 = 160

160 / .35 = 457.142857

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it