Question

Josh travels frequently. For a particular airline, it takes 20 minutes for the first bag to arrive in baggage claim after a flight. Bags then continue to arrive in baggage claim in steady succession over the next 10 minutes. The density curve below models the amount of time it will take for Josh to receive his bag.
A) What proportion of the time does it take longer than 27 minutes for Josh’s bag to arrive in baggage claim?
B) What proportion of the time does it take longer than 27 minutes for Josh’s bag to arrive in baggage claim?
C) What percent of the time does Josh’s bag arrive in less than 22 minutes?

Answer 1

Using the uniform distribution, it is found that:

A,B) 0.3 of the time does it take longer than 27 minutes for Josh’s bag to arrive in baggage claim.

C) 20% of the time does Josh’s bag arrive in less than 22 minutes.

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An uniform distribution has two bounds, a and b.  

The probability of finding a value of at lower than x is:

$P(X < x) = \frac{x - a}{b - a}$

The probability of finding a value between c and d is:

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

The probability of finding a value above x is:

$P(X > x) = \frac{b - x}{b - a}$

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• In the graph, we have that the distribution is uniform between 20 and 30 minutes, thus $a = 20, b = 30$

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Itens a and b:

• Above 27 minutes, thus:

$P(X > 27) = \frac{30 - 27}{30 - 20} = 0.3$

0.3 of the time does it take longer than 27 minutes for Josh’s bag to arrive in baggage claim.

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Item c:

• Less than 22 minutes, thus:

$P(X < 2) = \frac{22 - 20}{30 - 20} = 0.2$

0.2*100 = 20%

20% of the time does Josh’s bag arrive in less than 22 minutes.

A similar problem is given at brainly.com/question/15855314