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The auto parts department of an automotive dealership sends outa mean of 3.9 special orders daily. What is the probabilitythat, for any day, the number of special ...

Question

The auto parts department of an automotive dealership sends outa mean of 3.9 special orders daily. What is the probabilitythat, for any day, the number of special orders sent out will beexactly 4 ? Round your answer to four decimalplaces.

The auto parts department of an automotive dealership sends out a mean of 3.9 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 4 ? Round your answer to four decimal places.



Answers

Phone Inquiries The average number of phone inquiries per day at the poison control center is 4. Find the probability it will receive 5 calls on a given day. Use the Poisson approximation.

Okay, let's start. So first, let's understand the question. So we're given that ultra mobile cells person finds the probability off making a cell to be 0.21 So in the other case, it will be a no. So So if she talks to four customers, what's the probability that she makes four cells? So here she is coming to talk to the first cell person, first person she's or get a no cell or a cell. So this cell is 0.21 probability, and now she comes to talk to the second person again. There will be a probability that she gets no so and probably she gets the sale. And once again we are given that cell probability is 0.2. What? And once again, she come talk to the third person. Same thing over here again. Still is 0.21 and finally comes to talk to Ford Person. Once I get to sell, it still point to one. Since we're given that cell is still point to one probability fourth person. So if we want to find the probability that she make four cells all the way down here, four cells. We see that each cell has a probability of 0.21 And we see that each case off the cell, they are independent, they're independent. So using our multiplication rule, if we want to know the probability off getting a four cells right here, four cells, we would have to multiply our probability in this case 0.21 four times. And using our calculator, we find the answer to be zero point 001 night four or if we express it us a percentage, it is zero points one night for percent. So is this likely or unlikely? Obviously, with such a low percentage probability, it will be unlikely. And that's it for the question. Thank you.

To find the probability of an event. We take the number of favorable outcomes and divided by the total number of outcomes. So in this problem, we're finding the probability that Donovan visits an out of state college if you randomly selects from 10 out of state colleges and foreign state colleges. So the number of favorable outcomes would be 10 because he has 10 out of state colleges on his list and the total number of outcomes would be 14. Because there are 14 colleges on his list altogether. Let's reduce that fraction, and we get 5/7 and that's the probability that he will visit and out of state college. And then we can convert that to a decimal. We're going to have to round it to three decimal places, and we get 30.714 as the probability of visiting and out of state college

Okay, because in this problem, we're told that 35% there's a 35% probability that a student is interested in protecting their online privacy and the problem as us to find the probability that had a four randomly selected students. What is the probability that none of them, zero of them want to protect their privacy? And so, in order to answer this question, we need to determine the probability of a person not wanting to protect their privacy. Well, the probability of a person interested in protecting their privacy is 35% or 0.35 So that means the probability of a person not interested in protecting their privacy is one minus 0.35 or 0.65 So this is the key, probably the key number that we need, because we know we want to find the probability that out of four randomly selected students, what is the probability of zero of them want to protect their privacy? So if we do that, we know we're going to multiply 0.35 to the zero of power. Because zero students wanted zero students want to protect their privacy and we're gonna multiply 0.65 times itself four times because all four of them do not want to protect their privacy. And that probability is your 40.65 And we also want to multiply by four choose for just so you guys. The reason why I'm writing it out like this is just so you guys get a general idea of what we're doing in the long term process because every problem that you solve in probability, you have to tackle with this mindset tackle with the mindset of how many people are interested in the event that you have the probability for how many people are not interested and the different arrangements that can occur. The reason why four choose war in this matter doesn't matter. That much is because the number of ways you choose four people out of a group of four people is just one way. So that means all of these students don't want to protect their privacy or none of them do. That means there's only one way, and if you evaluate this, the four choose four evaluates toe 10.35220 Power values to one. So you're just multiplying by 0.65 to the fourth power. Now, this could have been your first step. How? I just wanted to walk you guys through from the from this work use for times 0.35 to 0 with times 0.65 to the fourth down to this stuff. So if we solve points expired to the fourth power, you will get that. Our probability is zero is 0.1785 and that's our final answer.

Starting with problem A. We want to find the probability that no more than four cars will be serviced. So we want to find the probability the X Is greater than or equal to four. Yeah, we do this by finding the probability of three which is point 12 plus The probability of x being equal to four. Or the how many cars are serviced on such a given day. So that would be p of 0.1 night. So X would equal for So this is x equals three And this is x equals four, which would equal 0.31 So to find the probability that a mechanic Services no more than four cars, you would take the probability of X equals three plus the probability of X equals four. For the next problem, you want to Find the probability that he will serve as fewer than eight cars. So you would do the probability of X greater than eight equals. And for this problem you want to do one minus the probability of X being greater Being less than or equal to eight. And all you're going to do for this problem is you're going to take all of your values and add them together from 1-7 and you'll get a number or you can do another thing. And this is easier. You can take the last number that fits in this parameter and the only number that fits in this parameter Is Equal 2.07. So you do 1 -17 equals 0.93 And that's what you're doing for the first numbers too. You're fighting the probability of some arbitrary parameter which is x equals three And x equals four for this one for part A So for the last question, part C We want to know the probability that we want to know the probability That he will service three or four cars, which is equal to be X equals three plus the probability of X equals for which is 0.12 plus 0.19 equals 0.31


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