b) what is the probability that in the next six flights two or fewer will be on

Question

b) what is the probability that in the next six flights two or fewer will be on time?

c) what is the probability that in the next six flights, at least four flights will be on time?

d) what is the mean and the standard deviation for this distribution?

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 83.9%. Complete parts a through e below. a. What is the probability that in the next six flights, exactly four flights will be on time? The probability is (Round to four decimal places as needed.)

Explanation / Answer

X ~ Binomial (n,p)

Where n = 6 , p = 0.839

Binomial probability distribution is

P(X) = nCx px ( 1 - p)n-x

a)

P( X = 4) = 6C4 0.8394 0.1612

= 0.1927

b)

P( X <= 2) = P( X = 0) + P( X = 1) + P( X = 2)

= 6C0 0.8390 0.1616 + 6C1 0.8391 0.1615 + 6C2 0.8392 0.1614

= 0.0077

c)

P( X >= 4) = P( X = 4) + P (X = 5) + P (X = 6)

= 6C4 0.8394 0.1612 + 6C5 0.8395 0.161 +6C6 0.8396 0.1610

= 0.9430

d)

Mean = n * p

= 6 * 0.839

= 5.034

Standard deviation = sqrt(n * p * (1-p) )

= sqrt( 6 * 0.839 * 0.161)

= 0.9003

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