Answer :
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:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
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- In the graph, we have that the distribution is uniform between 20 and 30 minutes, thus [tex]a = 20, b = 30[/tex]
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Itens a and b:
- Above 27 minutes, thus:
[tex]P(X > 27) = \frac{30 - 27}{30 - 20} = 0.3[/tex]
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:
[tex]P(X < 2) = \frac{22 - 20}{30 - 20} = 0.2[/tex]
0.2*100 = 20%
20% of the time does Josh’s bag arrive in less than 22 minutes.
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