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Homework Help: Statistic

Posted by Anonymous on Friday, January 25, 2013 at 12:50pm.

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
  
  Therefore:
  mean = .94n
  standard deviation = √(n)(.94)(.06) = √(.0564n)
  
  Using z-scores:
  z = (x - mean)/sd
  With the data:
  1.645 = (160 - .94n)/√(.0564n)
  
  Solve for n.
  
  (Hint: Round answer to 165.)
  

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