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1 month ago
14

The baggage limit for an airplane is set at 100 pounds per passenger. thus, for an airplane with 200 passenger seats there would

be a limit of 20,000 pounds. the weight of the baggage of an individual passenger is a random variable with a mean of 95 pounds and a standard deviation of 35 pounds. if all 200 seats are sold for a particular flight, what is the probability that the total weight of the passengers' baggage will exceed the 20,000-pound limit?
Mathematics
1 answer:
babunello [11.8K]1 month ago
8 0

Averages indicate 95 pounds per passenger with a standard deviation of 35 pounds, so multiplying this by the total passenger count of 200 gives the result of:

total average = 95 * 200 = 19,000

total std dev = 35 * 200 = 7,000

 

To find the z score:

z = (x – u) / s

here x represents the observed value = exceeding 20,000; u stands for the mean value = 19,000; s is the standard deviation = 7,000

 

z = (20,000 – 19,000) / 7,000

z = 0.143

 

Referring to distribution tables,

P (z = 0.14) = 0.5557

 

<span>Thus, there is a 55.57% likelihood that the total weight will surpass the 20,000-pound threshold</span>

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