A governments department of transportation reported that in

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 0.838.

Complete parts (a) through (e) below.

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 time?

c. Using the binomial distribution, what is the probability that in the next six flights, 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

The mean of the number of on-time arrivals is:__________

e. What assumption(s) do you need to make in (a) through (c)? Select all that apply.

Each observation is classified into one of two mutually exclusive and collectively exhaustive categories.

B.The probability of an observation being classified as the event of interest,,is constant from observation to observation.

C.The outcome of any observation is dependent of the outcome of any other observation.

D.The outcome of any observation is independent of the outcome of any other observation

Solution

b(x; n, P) = _nC_x * P^x * (1 – P)^{n – x}

^{A) 6}C4*P4*(1-0.838)²

B)6C6*P⁶(1-0.838)⁰

C)6C4*P⁴*(1-0.838)²   + 6C5*P5*(1-0.838) + 6C6*P6

d) Mean = 6*0.838