Answer:
The probability that the cycle time exceeds 65 minutes is .
∴ .
Step-by-step explanation:
Given that the cycle time for trucks to uniformly distributed over the interval (50,70)
Let Y be the random variable for cycle time
<h3>To find P(Y>65|Y>55) :</h3>
We know that The density function is inversely proportional to the length of a interval for a uniform distribution ( and 0 elsewhere)
The formula for Conditional probability is
Now we have that
<h3>Now we have to first find P(Y>65|Y>55) :</h3>
We have the common interval between interval Y>55 is (55,70) and Y>65 is (65,70)
∴
∴
∴
The formula
So we can write as
Since y∈(50,70)
∴
Similarly we find P(Y>55)=P(55<Y<70)
∴
( substituting the values)
∴ .
The probability that the cycle time exceeds 65 minutes is .