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Suppose that the value of a stock varies each day from$19 to $28 with a uniform distribution.(a) Find the probability that the value of the stock is morethan $21. (...

Question

Suppose that the value of a stock varies each day from$19 to $28 with a uniform distribution.(a) Find the probability that the value of the stock is morethan $21. (Round your answer to four decimal places.)(b) Find the probability that the value of the stock is between$21 and $26. (Round your answer to four decimal places.)(c) Find the upper quartile; 25% of all days the stock is abovewhat value? (Enter your answer to the nearest cent.)$ Draw the graph.(d) Given that the stock is greater than $2

Suppose that the value of a stock varies each day from $19 to $28 with a uniform distribution. (a) Find the probability that the value of the stock is more than $21. (Round your answer to four decimal places.) (b) Find the probability that the value of the stock is between $21 and $26. (Round your answer to four decimal places.) (c) Find the upper quartile; 25% of all days the stock is above what value? (Enter your answer to the nearest cent.) $ Draw the graph. (d) Given that the stock is greater than $20, find the probability that the stock is more than $25. (Round your answer to four decimal places.)



Answers

Suppose that the value of a stock varies each day from $16 to $25 with a uniform distribution.
a. Find the probability that the value of the stock is more than $19.
b. Find the probability that the value of the stock is between $19 and $22.
c. Find the upper quartile - 25% of all days the stock is above what value? Draw the graph.
d. Given that the stock is greater than $18, find the probability that the stock is more than $21.

Remember 68 question number, eh? Um quickly Number, eh? We are tryingto get her mind. Deter mined at the war. The worth off the stock off the stock after the first, The first Be okay. So, uh, if we can try confronted, the gain is $1000 plus 1000 dollars a month for Brian. By the 30% it was equal 1 1303 $100 the last the last is equal to one thousands. 1000 brothers. Ah, minus 1000 brothers. Or the percentage when something rollers right by 25%. Last. So the loss is 757 $150. Okay, so now we are trying to deter mined mind the wars off of the stock after the seconds. Second b. Okay, so here, if we have coup gains gains, it's equally cool. $1300 plus $1300 times. And the percentage with these 30% who is 16 and $100 if we have again. Gin on the second is loss. So and we will have when something 300 minus $1300 a month. The growing by the 25% um, 25% loss. So is the largest 975 minutes. Implant dollars. If we have two losses. Ah, so I wouldn't have to 150 have minus 50. Mother growing by 25%. So the final in 62.5 $0.5. Okay, so now we are trying to find the possibilities for this. Ah, loss or gains. Okay, So, uh, now we're trying to find the probability off each outcome is equal to the first again. And then a loss is a theme as obtaining first loss. And then again, So if we're trying to find the probability off, um, text 16 90 on donors, uh, 16 and 19. Ah, 16 $90 which is two games. It will be one over for two. It's going to five. Okay. And probability that 975 donors, which is one gin or one loss switching over for which is opening. Try is open for open five. And the probability that two losses s 562.5 on dinner. So it's equals two, one over over for opening. This is over four. Because as we said first again and they're lost is a simple reality Off first lost and then having G That's the one we we hear Ah Poot tu over over four Because the first loss and the second game is equal to the first game and second and second loss Okay, then if we, um trying to find the probability of X bigger than one some events donors. Okay, it is 11 possibility for extra be over, then when something which is 16 and $19. So the probability it will be over $1000 is equal to a probability it will be a 16 90. So the variety of X and bigger than my son and brother Diesel going to open to fight This is question this question number number a k. It's moved to question Number B and the question number be here, and it's trying to find the expected value. So here, coaching me and the expected they expected Vega and we know that, as expected, raining and mean or the mean wedding is equal to the sum of X Ah, multiplying by for ability off these X right so we can see that is equal to and it is equal to all the possible planets wants to use. The first is 16 19 million, but, boy, it's probative. It's opening for five. Hey! Plus 9 +75 And by its probability, which is opening five. Yes, on the lost value, which is 562.5. I'm not the Brian boy. It's a great pity opening too. 1 to 5 to the finance. For that is one being run and 50 points. 6 to 5 at others. And this is expected Value poor for the money. Thank you.

All right. This question deals with the distribution of stock prices with a mean of $30 a standard deviation of $8.20. So part eh wants the probability that a stock is more than $40 so that is equal to normal. CDF are lower bound, in this case is 40 and we want the area between 40 and infinity. So a large number and our mean is $30 our standard deviation is a point to, and that works out to be 0.1113 Part B asks for the probability that a stock costs less than $20 which is again normal CDF of a very small number. Very large negative number, I should say negative tend of the tent and our upper bound is 20 and we have the same mean and standard deviation as last time, and that turns out to also be 0.1113 And if that's a coincidence, don't be too shocked because 40 is one standard deviation above the mean, while 20 is one standard deviation below. So do the symmetry of the bell curve. They should be equal part, See, asks for to be in the top 10% which means that the area to the left equals 0.9 because if you're in the top 10% that means 90% must be below you. So we can use in verse and warm here with our area to the left and are mean and standard deviation. And that tells us that the top percent of stocks have a value greater than or equal Thio 40 point 51 dollars.

In this problem, we're going to be considering the box and whisker plot Shin to answer a few questions so that their bosques and weeks upon whisker plot is used to represent on individual stock that was selected and random from portfolio. So the first part of the problem A. We're finding the probability that the stock price ISS less than $21. So this, um $21 is here. So if we're checking for the probability that the stock price is less than $21 then we're just checking for the science in between these two dots. So And as you notice that there are four sections and each section represents 25% off the population. So let's see, this is 25% 25% thesis party is 25%. And lastly, thesis is 25% because thesis our quarters splitting the data set into form equal sections. So the probability that the stock price is less than 21 dollars eyes given by 25% in the second part of the question be we're finding the probability that the stock price is between $21.50 dollars so if you can notice, this is 20 between $1 and this is $50 and in between we have 25% and another 25% and all together we have 50% off the data set on. Therefore, the probability is 50% that the prices between $21.50 dollars Next. The last part of the question. See, we're supposed to find the probability that the stock price is $30 or more. So we go and check. We have $30 Markey's and we find it here. So if it started dollars or more so we can check the remaining part off the box and whisker plot. So and that takes out the 25% on the remains and 5% on In total. It's 50%. Therefore, the probability that the stock price is $30 or more is actually 50%

Mhm. Welcome to enumerate. So in the cutting problem we are told that the weekly amount of money spent on maintenance of repairs by a company is being observed and that follows a normal distribution. That means something sigma or standard division something. So it's very basically for us to say that X. Whatever it is it follows normal with mean this and is D. As $20. So what is X. The what is the meaning is about it's the on an average it's the amount that gets spent for maintenance and repairs. So we can write X. Is the random variable which is weekly amount off maintenance. Bye. Uh huh. Company that means this weekly amount of money spent on maintenance by your company is the random variable over here. Now they have asked what is the probability that the actual cost? That means in reality when they're having somebody they might spend 400 someday they might spend 380 someday it can be less someday it can be more someday it can be exact 400 right all these things. So what is the actual cost? What is the probability that the actual cost will exceed? For $50? So for that we can right the actual cost to actually be clear amount is X. So X. Greater than equal to 4 15. Okay now here we will we we can take help of the standard normal right variable. So we standardize, this is the way we standardize both decides are equally direct. So we can then right probability this is nothing but said greater than equal to 450 minus mean is 400 variances 20. So that would give us probability zero greater than equal to 50 by 20 which is 2.5. Now how will we find the value of 2.5. C. Here it is 2.5 is over here. So this is the probability that we are looking. So the probability is 0.6 two. This is the answer. Mm So now this answer is being obtained by So this is the probability if you ask, Okay, this is this. And this is from the table. From the table. We are getting this correct Sorry. From the table means it is property or uh support it and then it's a part B. They're asking that why why will we call this as equal? Okay. How is it happening? So let me show you the impact of standardization. So I suppose this is our standard normal. They did it. So that means what it is symmetric about zero and something over here is plus three. Someone over here is minus three. And it's symmetric and the total area under it is one and for normal good. No, it's possible that the same variable may lie over here. If I just add suppose five with each value. So basically this first variable, if that was the original variable. If I just add five with that, I will get a new set of values, right? So zero will come at five, so the zero will come at five. This three will go out eight and this minus three will come to cool. But yet again we will have the same good because this in this new axis probability of the X greater than equal to eight will be described everything. Got it and that will be in the old skill that will be called to this. So if I just probability zed minus five x minus five of them, it was eight minus five. If I do it, if you seek that minus five X minus five it's nothing but zero. So I can write zero greater than equals to three. So this is the concept of a plate properties and which has been already utilized in our current answer over here the moment we're standardizing, see we're subtracting the mean. So one might argue that what about the sigma? The sigma will also not impact. So it's a linear transformation. So so this this is the first this this one is the Z axis. Get it. And this part was exactly so kind of I can then there. Yeah. Girl said they take sure. Mhm. Um And suppose this is the Z axis and this is the X axis. So what it is, if this is zero. Okay. And if this is X then Z will be x minus 400. Bye. 20. Great. So in this case the same curve, even though there is a difference between the values. But these two straight lines are same because of this linear relation. And that's how these two label values. Say for example, over here there's that values and over here the X values. Even though there are different, the probabilities are same and why the difference? Because there has been a mean of 400 here, it is zero. But over here it is 400. That's the difference. So that's how the skills are different because of the mean and standard to be issued. So I hope this was understandable. If you have any questions, let me know. Bye bye.


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