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(A) The number of mobile phones sold daily atMEGA electronics has the following probability distribution.X: # of mobiles sold18192224P(X=x)0.40.20.30.1What is the m...

Question

(A) The number of mobile phones sold daily atMEGA electronics has the following probability distribution.X: # of mobiles sold18192224P(X=x)0.40.20.30.1What is the mean of the number of mobiles sold on a givenday?What is the variance of the number of mobiles sold on a givenday?

(A) The number of mobile phones sold daily at MEGA electronics has the following probability distribution. X: # of mobiles sold 18 19 22 24 P(X=x) 0.4 0.2 0.3 0.1 What is the mean of the number of mobiles sold on a given day? What is the variance of the number of mobiles sold on a given day?



Answers

The number of suits sold per day at a retail store is shown in the table, with the corresponding probabilities. Find the mean, variance, and standard deviation of the distribution. $$ \begin{array}{l|ccccc} \text { Number of suits sold } X & 19 & 20 & 21 & 22 & 23 \\ \hline \text { Probability } P(X) & 0.2 & 0.2 & 0.3 & 0.2 & 0.1 \end{array} $$

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.

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.

In this question, we are given ah poll redistribute probability distribution and we've given it in a table so we don't need toe do are in table So we have a value of X on picks the values of x 10 11 12 That scene on 14 on our probability X there's no point full no point to no point to again no 0.0.1 and not what one again. So we are asked to find the main and standard deviation. So to find the mean wings do x times p x So 10 times no point for is full 11 times No point to is 2.2, 12 times not 20 is to print full, sir scene times no point Well is 1.3 I'm 14 times no 140.1 is one point false. Remember, we're times ing these numbers by these so you just go down in the on So we get over, I use off x p x. And to get the mean we need our total so far probabilities, they total two bomb. So for this we need to some although things in this road. So we're gonna have four plus 2.2 plus 2.4 plus 1.3 plus 1.4, which gives us a total of 11 0.3. So this no the expectation of X which is also known as to me. To get the standard deviation, we'd first get variants and get variants. We first need to know X squared times p of x. So turn squared is 100 and 100 times about 1000.4 is 40 11 squared is 121 121 times. No point to 24 went to twelves Grad is 144. That time is not point to is 28 point eight the teens were This is a good test of your times. Tables 169 and that time is not quite one is 16.9 with 14 squared is 196 and that times 0 00.1 is 19 0.6. So now Justus, we did above. We need to get our total. So in two out of 40 24.2, 28.8, 16.9 onda 19.6. And if we some of those together with 129 0.5. So now in remember that the variation of X is the expectation of X squared, which is this number head minus expectation of X, which is all mean and we square it. So we've got 129.5 minus 11.3 squared on 11.3 squared is a home trying to 7.6 knowing I'm gonna put 11.3 squad Just remind you where I got that number from. So now we need to do that hunk in 29.5. Take away 127.6 night and we get a variation of 1.81 So last you need to do is look, that stunt innovation is the root variance. So we need to root. Need to root. Ah, one point eight. Well, on this comes out as one point three for five to three decimal places on that, it just

Based on this problem, we know that a cell phone has a lifetime average of being 24.3 months with a standard deviation of 2.6 months. And this is information dealing with the population of cell phones. And in this problem, the company is going to provide 33 employees with the cell phone. So, in essence, we're drawing a sample of cell phones from this population with the 33 cell phones, and the question is asking us what is the probability, or find the probability that they mean, which is the X bar is less than 23.8 months. So because we're talking about a sample of 33 people getting cell phones and we want the distribution of the average of those cell phones were going to apply the central Limit Theorem and the Central Limit Theorem says that the average of the means is the same as the average of the population, which is 24.3, and the standard error of the mean, or the standard deviation of the means is the same as the standard deviation of the population divided by the square root of end. So that's in this case going to be a 2.6 divided by the square root of 33. So we're going to want to draw an image, a bell shaped curve to reflect the problem. And we always put our average in the center and are averages 24.3. And the problem is asking us about being less than 23.8. So we're talking 23.8 right here, and we want to go less than so. The next thing we're gonna need to do is we're going to need to find the Z score associated with 23.8. So the Z score would be 23.8 minus 24.3, divided by standard error of the mean We should be 2.6 over the square root of 33 and the Z score turns out to be approximately negative 1.10 So the 23.8 is negative 1.10 meaning it's 1.10 standard deviations below the mean. So what we can do is we can rewrite this problem instead of talking in terms of the X score we can say that the probability that the averages less than 23.8 is no different than the probability that the Z score is less than negative 1.10 And at that point we would go to the standard normal distribution table in the back of your textbook and the probability that the Z is less than negative 1.10 is 0.13 57 So, to recap, our answer. The question waas that if we give cellphones to 33 people, what is the probability that the average of those 33 cell phone less less than 23.8 months and your answer be 0.1357?


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