A government\'s department of transportation reported that in 2009, airline A le
ID: 3338389 • Letter: A
Question
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%. Complete parts a trough 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.) b. What is the probability that in the next six flights, two or fewer will be on time? The probability is Round to four decimal places as needed.) C. What is the probability that in the next six flights, at least four flights will be on time? The probability is Round to four decimal places as needed.) d. What are the mean and standard deviation for this distribution? The mean of the number of on-time arrivals is Type an integer or a decimal.) The standard deviation of the number of on-time arrivals is Round to four decimal places as needed.)Explanation / Answer
p = 0.83
n = 6
P(X = x) = 6Cx * 0.83x * (1 - 0.83)6-x
a) P(X = 4) = 6C4 * 0.834 * 0.172 = 0.2057
b) P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 6C0 * 0.830 * 0.176 + 6C1 * 0.831 * 0.175 + 6C2 * 0.832 * 0.174
= 0.0094
c) P(X > 4) = P(X = 4) + P(X = 5) + P(X = 6)
= 6C4 * 0.834 * 0.172 + 6C5 * 0.835 * 0.171 + 6C6 * 0.836 * 0.170
= 0.9345
d) mean = n * p = 6 * 0.83 = 4.98
standard deviation =sqrt(n * p * (1 - p)) = sqrt(6 * 0.83 * 0.17) = 0.9201
e) Option-B)