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 51 lb and a standard deviation of 23 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

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 51 lb and a standard deviation of 23 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.)

With n = 100, the total weight exceeds the limit when the average weight x exceeds 6000/100 =60 lb

Standard error =sd/sqrt(n) =23/sqrt(100) =2.3

Z value for 60, z=(60-51)/2.3 =3.91

P( x >60) = P( z >3.91)

= 0.0000461

=0.0000 ( four decimals)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.