Question

Based upon past flight data, the average weight of checked baggage was 44.5 pounds with a standard deviation of 3.6 pounds. Weight of checked baggage was normally distributed.

Any checked bag weighing more than 50 pounds requires an additional charge of $95. For a flight with 400 checked bags, approximately how many bags will require an additional charge? (show work/explain please)

  

Answer 1

P ( X > 50 ) = 1 - P ( X < 50 )
Standardizing the value

Z = ( 50 - 44.5 ) / 3.6
Z = 1.53

P ( Z > 1.53 )
P ( X > 50 ) = 1 - P ( Z < 1.53 )
P ( X > 50 ) = 1 - 0.937
P ( X > 50 ) = 0.063

For 400 checked bags 400 * 0.063 = 25.2   25

Hence 25 bags would require an additional charge.