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4 The time (in minutes) that a customer spends with a bank employee to get serviced is distributed with the exponential distribution with parameter O= 2. For a give...

Question

4 The time (in minutes) that a customer spends with a bank employee to get serviced is distributed with the exponential distribution with parameter O= 2. For a given customer; what is the probability that he will spend less than 5 minutes with the bank employee to get serviced?

4 The time (in minutes) that a customer spends with a bank employee to get serviced is distributed with the exponential distribution with parameter O= 2. For a given customer; what is the probability that he will spend less than 5 minutes with the bank employee to get serviced?



Answers

The amount of time required to serve a customer at a bank has an exponential density function with a mean of 3 minutes.
Find the probability that serving a customer will require more than 5 minutes.

In this question here we recorded that if we have the X for on the exponential with the Recai, then it has the density F x you go to the gate times evil minus K x for the express equal to zero and the expected for all of the X equal to one of a gay in this question here were given the exhale stands for the seven time Yeah, and Exhale follows the exponential with the right. With the main, we go to three minutes. So from here means that the am the X equal to three on by the formula. Here we go to one of the K. They found the cave equal to one of the three here when again the gay we can find it and stay on the X and we go to one number three each of about minus x over three x credit equal to zero. Now I want to find a probability that the seven time it will be less than two minute here. So this is equivalent to the probability that under X here will be smaller than two. And given then the density function doesn't equal to the integral Studying from zero after the two here and now 103 age the minus X under 33 x and we get this one we ico thio entirely refuted reason Ik Ojeda minus Eva minus X out of three, evaluated from the to do so and until we get equal to the minus evil minus two and three and is there going to go to bless one? Therefore, we can write this now into the one minus evil minus two and three on this will be the answer. I'm the probability we're looking for.

Hey, it's Claressa when you right here. So you know the exponential density function it's f of X is equal to zero for one X is less than zero mu to the negative one e to the negative X over a meal when X is bigger or equal. Who's there? Oh, and were given that meal is equal to 30. So that makes f of X B equal to won over 30 e to the negative x over 30. Okay, we're gonna calculate being the probability the X is less than or equal to 15. This is equal to the integral from 0 to 15 for this function. One over 30 Hey to negative X over 30 t x. This gives us negative me to a negative X over 30 from the road to 15 which is around 0.393 for part B. We're going to do the same thing, but it's gonna be bigger, were equal to 16 or finding the probability for that. So this is equal to the limit. Must be approaches Affinity from 60 to be for one over 30 e to the negative. X over 30 d x. This becomes equal to around point 135 Princey, we're gonna do when p is he of X this equal to 300. So this is just the end to grow from 303 100 and then we just substitute our equation and we get zero our equation right here, one over 30 e to the negative expo. We know that anything like, since there's no interval, it's gonna be quick and zero. Now we're going to find the probability when X is bigger or equal to 1 80 because this equal to integral from 1 80 to infinity won over 30. Eat the negative X over 30 t x. This is equal to limit our be approaches Infinity for e negative e to the negative x over 30 from 1 82 b and we get around point 00 to 5 when we do one minus 10.25 and we get around 0.9975 So it is likely got all 200 customers are gonna be served within the three minutes


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