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The following the discrete probability distribution Find Ihc misring probability-enablc0.12The number of overtime houre (0) Lorkcd one weck pcr ciployec - Waldeo 9 ...

Question

The following the discrete probability distribution Find Ihc misring probability-enablc0.12The number of overtime houre (0) Lorkcd one weck pcr ciployec - Waldeo 9 j6 recorded blow Note that employecs rzy nut work a Fraction ofan hour ofovertimgQvcrtime Hours Kumher Oarmplorcc6.) Construct the probability distribution.Graph the probability distribution usine histogram and describc its shape,

The following the discrete probability distribution Find Ihc misring probability- enablc 0.12 The number of overtime houre (0) Lorkcd one weck pcr ciployec - Waldeo 9 j6 recorded blow Note that employecs rzy nut work a Fraction ofan hour ofovertimg Qvcrtime Hours Kumher Oarmplorcc 6.) Construct the probability distribution. Graph the probability distribution usine histogram and describc its shape,



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Construct a probability distribution, and (b) graph the probability distribution using a histogram and describe its shape. The number of overtime hours worked in one week per employee (TABLE CANNOT COPY)

You know this probably want to use the probability distribution that we made one problem. Number 20. Find the probability of randomly selected employees whose overtime hours is on a 2 to 3 hours. So the probability of two or three it's a probability of two, plus the probability of three. The probability of to is 29/1 92. Probability of three is 19/64 29/1 92 plus 19/64. Okay, is 43/96. So that's the probability of two or three on B. We want to find the probability of three hours or less probability of three or lessons. Probability of zero. It's probably of one probability of to awesome probability of three ability of zeros. 1/32 ability of one is 1/16 have ability of two is 29/1 92. The probability of three is 19/64 and so when I had these together, this gives us 13/24 on on C. You want the probability of between to and five is the probability of two awesome probability of three. What's the probability for What's the probability of Father? Probability? Of two is 29/1 92. Probably three is 19/64 probably a 4 7/32 on the probability of five is 5/32. That's when we have these together, this is 79 over 96.

So here we're going to meet the table for frequency distribution. Yeah. What? First column will be terrible, Will you not in FYI so intervals we have toe assign with size off five. So it will be starting from 0 to 4. You've been fasting time, then from 5 to 9. Second in Tamil, then from 10 to 14. The third interval. Then from 15. 90 and the last will be from 20 2 24. The last column we make for daughter. So next column will be frequency and frequencies the number off values that fall within that interval. So, for example, from 0 to 4, we will see how many How many numbers are falling between these two numbers. So there are four numbers for example, to four. Four are falling between these intervals. So eight numbers fall between five and nine. Five numbers fall between 10 and 14 Two numbers for with me 15 and 19 and only one number fall between 20 and 24. So when we will add them up where we had a total off 20. Next, we have to show relative frequency distribution cumulative frequency distributions, the frequency divided by total number off. Uh, total frequencies or total frequencies. 20. So when you will divide four by 20 you will get you don't find too, and so on. We will divide this number by total number of frequency. And we will We will add these values. We should get one. Then we have person frequency percent frequency in the relative frequency multiplied by 100. So it will be mhm. This number will give my 100. And then we we heard them. We should get 100. Then we will make another column. Far a cumulative frequency. So cumulative frequency the frequency increased by the frequency off previous class. So accumulating frequency for the first class will be four. Then you re adding eight with four. So we'll get 12 and so on. You will keep earning. Look, next column will be a cumulative relative frequency So cumulative, very difficult. NCI's The cumulative frequency divided by the total frequencies was for total frequency is 20. So four divided by 20 will be point to 12 invited 20 will be 200.6 and so on. So the last part is what portion of patient needing emergency service and with till nine years or less. So we will look at the, uh, cumulative frequency off the category 5 to 9 because it is adding them previous interval to. So we have got here 0.6 and we will when we will multiply little 0.6 bid 100 If you endured 60%.

Okay. This problem we have to properly function is One of the 1000. Each of the power of the negative x. Or 1000. And for here we have the distribution function. Is that So fx committee distribution function would be so record at X. Should be it should be good and dear. Okay. So it should be from the 1000 two X. So this fx dx Every calculate it should be elective. Each of how effective eggs over 1000 from X to zero. So the answer of the one minus into the power of negative X over 1000. This is the probability distribution the committed distribution function. And propose dad Actually screwed. And three Sowden would be So it's F 3000 minus F zero. And the answer would be to tell -3. And the answer is .0498. So that's the answer.

You know this problem? You refer back to this probability density function and we would like to find a cumulative density function for. Remember that you're a cumulative density function is equal to the integral in this case from zero to access because that's is always greater than zero here of our probability density function. And so here on this problem we have capital F of X Is going to equal the integral from zero. So that's of the end of the negative acts over a 1000 over 1000 dx. This is the negative integral. or in the negative be negative acts over a 1000 from X equals zero to act. This is bad notation. You're not really supposed to use an X in both places like that. It'll give us an answer. But it's just something to be aware. This gives us negative E. To the negative X. 4000 minus negative E. To the negative zero which is one minus E. U. To the negative acts over 1000. And so this is our cumulative density function. But it's only valid for X is greater than zero. Just like the media. Now, we do want to find it. This is X over to use it To find the probability that last more than 3000. So we want the probability that X is greater than 3000, which is one minus the probability that X is less than or equal to 3000 this year is the definition of F of three thousands. This is one minus capital F. Of 3000, which is one minus one minus E. To the negative 3000 over 1000 which gives us E To the negative third. So it probably lasts more than 3000 hours because even the negative third, which you can get as a decimal if you need. Mhm.


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