A govemment\'s department of transportation reported that in 2009, airline A led
ID: 3326419 • Letter: A
Question
A govemment'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 0.826. 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? The probability is (Round to four decimal places as needed.) b. Using the binomial distribution, what is the probability that in the next six flights, all six flights will be on time? The probability is (Round to four decimal places as needed.) c. Using the binomial distribution, what is the probability that in the next six flights, at least four flights will be on time? The probabilit is (Round to four decimal places as needed.) 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 (Round to four decimal places as needed.) The standard deviation of the number of on-time arrivals is (Round to four decimal places as needed.) Click to select your answer(s) C Chegg Study | Guided Solutio xExplanation / Answer
BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
a.
P( X = 4 ) = ( 6 4 ) * ( 0.826^4) * ( 1 - 0.826 )^2
= 0.2114
b.
P( X = 6 ) = ( 6 6 ) * ( 0.826^6) * ( 1 - 0.826 )^0
= 0.3176
c.
P( X < 4) = P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 6 3 ) * 0.826^3 * ( 1- 0.826 ) ^3 + ( 6 2 ) * 0.826^2 * ( 1- 0.826 ) ^4 + ( 6 1 ) * 0.826^1 * ( 1- 0.826 ) ^5 + ( 6 0 ) * 0.826^0 * ( 1- 0.826 ) ^6
= 0.0696
P( X > = 4 ) = 1 - P( X < 4) = 0.9304
d.
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 6 * 0.826
= 4.956
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 6 * 0.826 * 0.174
= 0.862344
III.
standard deviation = sqrt( variance ) = sqrt(0.862344)
=0.928625