An airplane with room for 100 passengers has a total baggage limit of 6000 lb. S

Question

An airplane with room for 100 passengers has a total baggage limit of 6000 lb. Suppose that the total weight of the baggage checked by an individual passenger is a random variable x with a mean value of 50 lb and a standard deviation of 20 lb. If 100 passengers will board a flight, what is the approximate probability that the total weight of their baggage will exceed the limit? (Hint: With n- 100, the total weight exceeds the limit when the average weight x exceeds 6000/100.) (Round your answer to four decimal places.)

Explanation / Answer

mean = 50 , s = 20 , n = 100
P(x >60)
By normal distribution,

z = ( x - mean) /(s/sqrt(n))
z = ( 60 -50) /(20/sqrt(100))
= 5
P(x >60) = P(z >3.5355) = 0. by using standard normal table

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