Respuesta :
Answer:
The probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 55 minutes, should be 1 / 3.
Step-by-step explanation:
It is known that the cycle times for a truck hauling concrete is uniformly distributed over a time interval of ( 50, 70 ). If c = cycle time, according to the question the probability that the cycle exceeds 65 minutes, respectively exceed 55 minutes should be the following - ' [tex]Probability( c > 65 | c > 55 )[/tex]. '
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[tex]f( c ) = \left \{ {{1 / 20,} \atop {0}} \right. \\50< c<70 - ( elsewhere )[/tex]
We know that the formula for Probability( A | B ) is P( A ∩ B ) / P( B ),
[tex]P( c > 65 | c > 55 ) =[/tex] [tex]P( c > 55[/tex] ∩ [tex]c > 65 )[/tex] / [tex]P( c > 55 )[/tex],
And now we come to the formula [tex]P( a < c < b )[/tex] = [tex]\int\limits^{70}_{65} {f(x)} \, dc[/tex]. Substitute known values to derive two solutions, forming a fraction that represents the probability we desire.
[tex]P( 65<c<70) = \int\limits^{70}_{65} {f(y)} \, dy\\ = \int\limits^{70}_{65} {(1/20)} \, dy\\ \\= 0.25[/tex]
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[tex]P( 55<c<70) = \int\limits^{70}_{55} {f(y)} \, dy\\ = \int\limits^{70}_{65} {(1/20)} \, dy\\ \\= 0.75[/tex]
Take 0.25 over 0.75, 0.25 / 0.75, simplified to the fraction 1 / 3, which is our solution.
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Probability: 1 / 3
