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Usual values for a probability distribution_ The sales records of a real estate agency show the following daily sales over the past 200 days_ Convert this frequency...

Question

Usual values for a probability distribution_ The sales records of a real estate agency show the following daily sales over the past 200 days_ Convert this frequency table into an empirical probability distribution, then answer the question: What is the maximum usual number of houses sold in one day? Round your answer to twQ decimal places_Houses Sold Number of Days5043(HINT: In order to find the max usual value, you need to start with / and &)

Usual values for a probability distribution_ The sales records of a real estate agency show the following daily sales over the past 200 days_ Convert this frequency table into an empirical probability distribution, then answer the question: What is the maximum usual number of houses sold in one day? Round your answer to twQ decimal places_ Houses Sold Number of Days 50 43 (HINT: In order to find the max usual value, you need to start with / and &)



Answers

Insurance Sales The amount of insurance (in thousands of dollars) sold in a day by a particular agent is uniformly distributed over the interval $[10,85]$ .
a. What amount of insurance does the agent sell on an average day?
b. Find the probability that the agent sells more than $\$ 50,000$ of insurance on a particular day.

The question Number 21 The corresponding distribution is a fossil distribution because on average, rate is given. That is not that possibility for which you would use the binomial Mr So The other tree. He's eight. I agree. 175 days and those you talk to a point Me? The average rate is equal to eight Boy 16 mhm. 275 equal to 90 Mhm 55 No, To that we multiplied by 60 over 275 because we have three days instead off 175. The formula off parcel distribution is See when xxx UK export to from the poverty by equal native Wanda over transition. So evaluate at okay because it was you. 14. It's equal to zero Mhm. No one can speak because always in my knee color me just like Jesus. 25 the victors in heat You What do you think? You 4.1714 6 Thank you. Because you're young 20. Thank you. Six told 55 Always one boy equal Just this story Bye over one for tradition equals 4.3 thousands in 27. So the component rule his for he will not a well, because one minus few things. So you the compliment food when X is greater than or equal to political to one month he accepted to zero plus minus. He's on Exhibit one is equal to one minus okay 100 sergeants and 746 to minus Opened 3000 And do what he said. Is it going too often? 5000 and 207. We're going to see the average rate physical toe. Eight boys 19 over 275 equal to 144 is 55. Note that we multiply by 90 over 275 because we have 90 days instead of 275. So we want to evaluate. It's okay if you 20 So for your next people to view is equal to 144 over 55. What would you like this for? The negative? 100. I'm 44. 55 over a factory vision to you. Well, approximate people opening told 729 40 when execute 21 Did you go to 154. 55 for one. Well, you need a good people and you give 124 approximately equal to four point 1910 for few on X equal to two, 144 over 55 are square, but people are negative. Another than 24 for so far. Bye. Transition tool Affectionate 4.2000 and 700. Using the compliment rules which is for people and not a as you go to one minus B If a using the continent roof for few and X is greater than or equal three is equal to one minus You've accepted to Is you mine was p off. Expect it one minus. You've expected to is equal to one minus opened. 700 and point Oh, 729 minus opening. 1000 and 110 minus four point. 200 500. 2500 Physical toe open. 2000 and 861. Thank you.

To find a ming and standard deviation. We first need to find the uh probability distribution. And so let's look for each case and their probabilities First, you're is a probability of 1/3 that There's only one customer and The probability of 2/3 that there are two customers. And if there is only one customer, There is a probability .1 that the contact will result in no seal and .9 that the contact will result in yourself and has this to number of the provide possibilities. And if there are two customers since these two sales are independent, so their distribution is a phenomenal distribution and we can use a formula bell nominal distribution And this 3 uh the probabilities of the phenomenal distribution, but also we need to time. The probability is that there are two customers Which is 2/3 in the hands. This uh the total probability. Now we can write the probability, so the probability of zero is this number plus this number, We just zero, awful. And the probability 50,000 is just as this number boss. This number And it's part for two. The probability of handover Selden The PIN 252. So now we can calculate the me and according to the formula is just as some oh The probability of wild times the value of one and it recalls zero times .04, clause 50,000 times point of 4 to plus a handler. Selden times point of forfar And the number is 75 seldom. You too calculated the standard deviation. We first calculate the veterans and various echoes the expectation of Y squared miners, the square of expectation, Why this? This is just me and the expectation Y squared. It's just that the submission of the proper detail, white times the value of y square and the value is 6.45 times turned through the power I'm not. And then we can calculate the barracks, which is 8.25 times central power of eight, and the standard division, just as the square root of the virus, which is approximately 28,000 722 points eight.

So this question, as the data have been given that mule is equal to four days and the standard division Sigma is given as one day. And then you didn't start at normal distribution concept so we can use the formal offset here, which is given by X minus mu upon sigma. And if I substitute the value here, this would be equal to X minus for born one. So now the first question is to find out the probability off X is greater than to not this part I can write down as one minus probability. Off X is less than equal group. So to find out the value of excellence, any point to where I need to find out that said value. So I had X is equal to do. We can find out said, which is true minus fall upon bond, which gives you minus two. So this will actually change to one minus the off there is less than equal to minus two. And, uh, this is from the table. We can ride one minus 0.28 And if you calculate the value of getting her this 0.977 so this was the first part that we've done off a little bit of second part. You say that suppose n is Ah, you said that, you know, the end of dreams should be protest. Okay. And, uh, therefore, you say that on average, wondering should and in 60 of one end ese But so I never write down that at X is equal to 60 upon in value. We're going to find out that so that everybody will do 60 or one in minus four. And the whole thing is divided by one. So now they've told us that this probably use 80%. So therefore, I don't that Thomas probability off Zed greater than equal 60 upon end minus four is given as 80% switches. Wind eight. So took. I feel this proverb gives a great Then you go. I can write down the says one minus probability off cell is less than equal to 60 our own and minus four, which is going eight. And now I've got to simplify its expression to find the value off zey. So if I do one minus 10.8, this will be equal to probability. Off there was less unequal toe 60 by end minus four. So this is 0.0 is equal to provide witty off their lesson. It could do 60 upon end minus four. Now you do this part, the value at Pointe Du from the table is going to be 0.8 for, so I have point off. 84 is equal to 60 upon and minus four. So therefore the answer is 60 opponent, which is equal to 4.84 I can capture the value of and therefore just equal to 60 a coin. 4.84 just giving me drill 0.39 And, uh so I can approximate this value and can see. Therefore, in total, there are 14 dreams.

Question here is essentially going to ask us about the mean variance, standard deviation and expectation here. So essentially what we're given is that were given a scenario where we have something related thio suit sales. So basically states here that the number of suits sold per day at a retail store is shown in that particular table with its corresponding probabilities. So it wants us to firstly find the means, variance and standard deviation. So in order to find the mean here, we are essentially going to find the average value between all of these and just based on deduction. And the relative probabilities, as their approximately equal here waken state that are mean is going to be essentially just the number of units sold X times. It's probability and just added up together, and that is going to give us a mean value of 20 point eight here in order to find the variance. The variance is essentially how spread the data is. So as you can see, it goes from 19 to 23 so essentially are variants is going to be, too, and our standard deviation here can essentially just be taken by our calculator and that is essentially just the variance squared. So in this case, it's going to be four here. So the actual question here asked us if the manager of the retail store wants to be sure that he has enough suits for the next five days how Maney should be manager, um, purchase here. So if we know that the number of suits sold per day on average is going 20.8, you could just essentially take back and multiply by five year to get a value of 104 which is going to be our average suits sold within the next five days, So this should be about enough.


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