Delivery trucks arrive independently at a distribution...

Delivery trucks arrive independently at a distribution center. The mean number of trucks arriving per hour is 17. Given that a truck has just arrived, use the Exponential distribution to answer the following questions. a. What is the probability that the next truck will not arrive for at least 5 minutes: P[t ≥ (5/60)]? b. What is the probability that the next truck will arrive within the next 2 minutes: P[t ≤ (2/60)]? c. What is the probability that the next truck will arrive within the next 3 minutes: P[t ≤ (3/60)]? d. What is the probability that the next truck will arrive between 4 and 10 minutes: P[(4/60) ≤ t ≤ (10/60)]?

Transcript

00:01 Hi, i'm david and i'm here to help you and see your question.

00:03 Now let me bring up your question here.

00:05 In the question here, we are going to discuss about the exponential distribution.

00:09 Let me remind you that if you have the x that follows by exponential, when the rate equal to the lambda, and then the density of x equal to the 1 lambda times e to the power minus lambda x for the x greater equal to the 0, and the community distribution function f capital on the x equal to 1 minus e to the power minus lambda x for the x squared equal to the 0.

00:38 In the equation here we have the x that will be the time between the tricks will arrive.

00:46 And we will have here the next trick will arrive.

00:51 So x, every condition will be the t, not the x.

00:54 So t will equal to into arrival time and then t will follow by the exponential when the lambda now equal to the 17 per hour.

01:12 And then in the first question a, asking you to find the probability that the t here will be quite equal to the five out of the 60.

01:25 And to find this probability here we can convert it into the cumulative decision function by writing this as a 1 minus the probability smaller than the 5 over the 60.

01:38 And notice that because under continuous random variable we can include the equal here.

01:44 And then we can get this one equal to the 1 minus the probability.

01:47 This one exactly will be the f of the 5 over 60.

01:56 And then in the excel we can write this down it will equal to the answer will equal to the one minus here we have expo and then dot this and we have the value here will be the 5 over 60 and then the rate equal to the 17 and this will be true stand for it will be the cumulative and we will do this one first and then i will go to the excel to show you how to compute it so so we will put this on equal first.

02:31 And for the question b, once you find the probability that the t will be small equal to the 2 of the 60.

02:41 So this one is exactly equal to the f of the 2 over the 60...

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