Question 1: If n = 7 and n = 0.35, what is the probability of the following?
a. X = 6
b. X ≤ 5
c. X < 4
d. X > 3
a. P(X = 6) =
b. P(X ≤ 5) =
c. P(X < 4) =
d. P(X > 3) =
Question 2: Assume a Poisson distribution.
a. If λ = 2.5, find P(X = 1).
b. If λ = 8.0, find P(X = 10).
c. If λ =0.5, find P(X = 0).
d. If λ = 3.7, find P(X =8).
a. P(X =1)=
b. P(X=10)=
c. P(X = 0)=
d. P(X = 8)=
Question 3: A government's department of transportation reported that in 2009, airline A led all domestic airlines in on-time arrivals for domestic flights, with a rate of 0.833.
a. Using the binomial distribution what is the probability that in the next six flights, four flights will be on time?
b. Using the binomial distribution, what is the probability that in the next six flights, all six flights will be on tine?
c. Using the binomial distribution, what is the probability that in the next six fights, at least four flights will be on time?
d. What are the mean and standard deviation of the number of on-time arrivals? Let n = 6
e. What assumption(s) do you need to make in (a) through (c)? Select all that apply.
A: The outcome of any observation is independent of the outcome of any other observation.
B: The outcome of any observation is dependent of the outcome of any other observation.
C: Each observation is classified into one of two mutually exclusive and collectively exhaustive categories.
D: The probability of an observation being classified as the event of interest, a. is constant from observation to observation.