An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a capacity of 160, if it wants the probability of accommodating all reservation holders to be at least 95%.
Statistic - MathGuru, Friday, January 25, 2013 at 5:22pm
Use the normal approximation to the binomial distribution.
mean = np
standard deviation = √npq
mean = .94n
standard deviation = √(n)(.94)(.06) = √(.0564n)
z = (x - mean)/sd
With the data:
1.645 = (160 - .94n)/√(.0564n)
Solve for n.
(Hint: Round answer to 165.)