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Given standart normal distribution, find value P(-0.93 < 2 < k) 0.7235_such that...

Question

Given standart normal distribution, find value P(-0.93 < 2 < k) 0.7235_such that

Given standart normal distribution, find value P(-0.93 < 2 < k) 0.7235_ such that



Answers

Given the standard normal distribution, find the value of $k$ such that (a) $P(Z>k)=0.9625$ (b) $P(Z<k)=0.6255$ (c) $P(0.17<Z<k)=0.367$.

For this question of a sample size of 24 and they have to find key, you know, degrees of freedom, Missy. Quote and manage when Israelis 20 for minus one. And this is 23 and we had elevated C distribution. And so the truth, Our area here, this one going to use this diagram to solve the question 50 here the total. Okay. From the question, I have negative 2.69 See, value. And that is that lies to the left of you. Now, for the distribution of total area to the right of zero is 0.5. The total area to the left off zero is 0.5. And the question gives us a value off 0.965 between two t values and because their value is more than 50% partof realized to the left and impartial eyes to the right. So this down would be my key. Well, you look up the value off. Praise your 69 from the tea distribution table. They're from the table. Cooper is your 69 inside are far level off 0.25 and interviews off them off 23. So I'm going to find a negative off this value that gets you negative. 2.69 Therefore, 0.25 is the area to the left off negative 2.69 and then are faced the area to the right off key. The total area here, this one. So when I add the areas up, I should go one. And this case, I'm going to do a letter. Bits off budget right here. So how far is it? Quote one minus zoo points 99 And the value is zoo point as you want. So well, you look up this value from the sea distribution table, the values 2.5 years you and so this value is the value off key. Now let's get to the next question. Parts be for parts B. The total every opportunity to value is 0.95 and I have a T value of 2.807 The area to the right of you is your 0.5. The area to the left of zero is 0.5. I'm going to look up a value from let's see distribution table from the distribution table offer. Level off. Super is your five with degrees of freedom off 23 gives me two points easier with seven. Therefore the area to the right of two points easier. 70.5 The question tells us that the area between point is your seven and then another value, which is key is 0.95 I noticed that when we added two values the Allessandro print for a free just way they lie to the right of you. So you're looking for the total area to the right off key and that would be our Alfa. So 0.95 plus 0.5 would be quote Alfa That issue coaches your prints when were to look at this value from the tea distribution table and that is equal to 1.3 a 19 Therefore, this value is the value off key to the next question at sea. I have zero here and then I have a key to the right key to the left. I mean, negative key to the left of you read to the right off zero is 0.5, and then the area to the left off zero is your brain's five. The question tells me that area between key and Negative Key is 0.9. Therefore, our farm to the left in the offer to the right in this case. So when I add the two office and zero point and zero points now, I should get one, have to off apply 0.98 is equal to one, and then I do a letter bits off algebra here and that issue quote 0.5 So when you look up this value from the city suspicion table, I have a value off 1.714

Okay, So what we're looking for is the probability that a random number lies within two standard deviations of the mean and refining it for any normal distribution. So I'll just draw out a normal distribution just so we can look at it. And that's kind of what it's gonna look like. And this will be the mean and we want two standard deviations to left into the right. Okay, so there's multiple ways of doing it. This the first way is to know that in any normal distribution 90 approximately 95% uh, the numbers are gonna fall within two standard deviations. So since we're looking for the probability, that would just translate to 0.95 But that's not super specific. So if you want on answer that goes to more decimal points. You want to be a little more specific with it. You can use the Z score, and so Z score equals the, um, your value. So we'll just call that X minus the man over the standard deviation. So we know that the value is to ST's, which were those away from the mean. So no matter what, it's just gonna be two standard deviations, and we can just call the means zero, because it's for any distribution. And so the standard deviation just cancels, leaving you with a Z score of just two. And if you have something called table A, you can look it up online, and it will show you all of the, um, corresponding um proportions for Z score of two so you can use that and you'll get around. You will get around 9545 and that is in decimal form because it's a probability, and so that is your more exact answer.

Okay, So what we're looking for is the probability that a random number lies within two standard deviations of the mean and refining it for any normal distribution. So I'll just draw out a normal distribution just so we can look at it. And that's kind of what it's gonna look like. And this will be the mean and we want two standard deviations to left into the right. Okay, so there's multiple ways of doing it. This the first way is to know that in any normal distribution 90 approximately 95% uh, the numbers are gonna fall within two standard deviations. So since we're looking for the probability, that would just translate to 0.95 But that's not super specific. So if you want on answer that goes to more decimal points. You want to be a little more specific with it. You can use the Z score, and so Z score equals the, um, your value. So we'll just call that X minus the man over the standard deviation. So we know that the value is to ST's, which were those away from the mean. So no matter what, it's just gonna be two standard deviations, and we can just call the means zero, because it's for any distribution. And so the standard deviation just cancels, leaving you with a Z score of just two. And if you have something called table A, you can look it up online, and it will show you all of the, um, corresponding um proportions for Z score of two so you can use that and you'll get around. You will get around 9545 and that is in decimal form because it's a probability, and so that is your more exact answer.


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