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An airplane with room for 100 passengers has a total baggage limit of 6,000 lb. Suppose that the...

Question:

An airplane with room for 100 passengers has a total baggage limit of 6,000 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 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.)

Normal Distribution:

When samples are selected from the population which is normally distributed then the distribution of sample means will also be normal regardless of the size of the sample.

Answer and Explanation: 1

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Total baggage limit {eq}= 6,000 \text{lb} {/eq}

Total number of passengers, {eq}n = 100 {/eq}

So:

Baggage limit per passenger:

{eq}\frac{6000}{1...

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Normal Distribution of Data: Examples, Definition & Characteristics

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