4. The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. What is the probability that the cycle time exceeds 65 minutes?

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

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

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 .

step-by-step explanation: