# 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.

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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... Normal Distribution of Data: Examples, Definition & Characteristics

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Chapter 13 / Lesson 7
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