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Given Sandardized noMa dislrbuticn (rid Mcall gtandard deviation = Click here vicw [Xa Ihe rumullaten "stiindardizcd nuxrnal distribution table_compleurAtChck ...

Question

Given Sandardized noMa dislrbuticn (rid Mcall gtandard deviation = Click here vicw [Xa Ihe rumullaten "stiindardizcd nuxrnal distribution table_compleurAtChck herepagecuntuat standamdized ncnlal dislbabon tabaWhatk obabilit; thatless than Probablty that = less Ihan nke600 56 Is [ (Round t0 four decana Narar

Given Sandardized noMa dislrbuticn (rid Mcall gtandard deviation = Click here vicw [Xa Ihe rumullaten "stiindardizcd nuxrnal distribution table_ compleur At Chck here page cuntuat standamdized ncnlal dislbabon taba Whatk obabilit; that less than Probablty that = less Ihan nke600 56 Is [ (Round t0 four decana Narar



Answers

Let $x$ be a continuous random variable with a standard normal distribution. Using Table $A,$ find each of the following. $$P(-2.45 \leq x \leq-1.24)$$

For this problem, you're going to use the applet for chi square probabilities and quantum files to find the probability that the sum of Z sub I squared Is less than or equal to six. And we're going to let I go from the values of one 26 and you need to recall or hint that the sum of Z squared sub i As I goes from 1 to 6 has a chi square distribution with degrees of freedom equal to six. So when you open up the applet you're going to see a chi square distribution and your chi square distribution is a curve that is skewed to the right. And at the top of that you're going to see a location where you can put in the degrees of freedom. And at the bottom you're going to see two locations, one where you can put in an X. Value and one where you can type in a probability. So since we are trying to determine a probability, we're going to leave this one blank and let the calculator or the applet generated. So we know that our degrees of freedom are six. So we're gonna put a six in here and we are trying to determine the fact that Z squared is less than or equal to six. So six is going to be right here on the curve. So we're going to put a six in here and remember what we're looking for is we are concerned with being less than six, so we are concerned with this area right here. Unfortunately, though the applet doesn't go and give you the area to the left instead, it gives you the area to the right. So when you're looking at your applet, you're going to see the area over here shaded in And it's going to generate a value and the value it's going to generate is going to be a .4-3. So that is telling you that the area right here is .4-3 and we know that the Curve, the entire curve, the area under the entire curve is equal to one. So we want this side, so we know that the side were interested in plus what the applet just gave us has to equal one. So therefore what we are interested in will be one minus 10.4 to 3. So we could say that the probability of the some of Z sub I squared as I is going from 1 to 6 being less than or equal to six will be a probability equivalent to approximately 60.577 Which is what we get when we subtract 0.4 to three from one.

In discussion. We re condon the cumulative That's the distribution function. F capital X echo to the integral from minus infinity up to the X after density Ever D d t. And in this question here were given the density function F X equal to 1/5 for the X in the interval from 2 to 7. And here we will be able to find against the function here the community functions. Have capital X. It got your integral form that you to the ANC's here on. We have a density here. Could be one of the five. The d is gonna be one of the five DT, and then we get ego to until you reverted. I'm the one of the five because you one of a five de on then evaluated attitude to X and they were looking the limit. Here we get there, uh, X over five minus 2/5. We can register into the X minus 2/5, and this one will be funded for the X in interval from 2 to 7. This when we read the cumulative distribution function we're looking for here


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