Assuming a random variable, x, has a normal distribution...

Transcript

00:01 Hey hello everyone this question is very important and interesting also that means what here it is given that the mu value which is 5 okay and the sigma value which is given here that is 0 .5 and this particular question we have three conditions and according to the conditions we have to find out the value of the right and the first condition is which is right written here that is probability of zero okay x in between the 0 to a and that value is 0 .17 and for that reason we have probability of condition that is x minus 5 divided by 0 .5, that is in between the 0 to a minus 5 divided by 0 .572.

00:45 And here the next step is probability of that 0, x minus 5 divided as 0 .5 is taken as z and the a minus 5 divided by 0 .5 which is taken as z dash is equal to 0 .17.

01:00 272 and now we are using the normal probability okay by using normal probability table okay what we are going to get that will write here okay one second okay so now the z -dash is equals to 0 .46 okay now the z -dess condition is what a minus 5 divided by 0 .5 right or not is equal to 0 .4 6 right and here we are calculating the a value and that a value will be very simple that is 0 .4 6 multiplied by 0 .5 plus 5 or added with 5 and that that a value is coming out as how much that is 5 .23 okay so this is the answer of this question that a value is 5 .23 okay after that we are going to calculate this second part or the second condition okay we'll read out of the condition first so the condition here it is given that probability of 8 which is smaller than from x that is equal to 0 .1539 right and we are going to write the condition okay so probability of a minus 5 divided 0 .5 which is smaller than that of the y minus 5 divided by 0 .5 is equal to 0 .1539 and a minus 5 divided by 0 .5 is taken as z and y minus 5 divided by 0 .5 is taken as z which is equal to again 0 .1539 right and here we changed the condition and that's very simple nothing else we just put the formula here okay that probability is equal a probability of z that is under bit under 0 to z dash which is equal to 0.

03:09 0 .5 minus or subtracted with 0 .1539 right and we are getting finally the value of probability of this that is 0 .3461 and now we are going ahead with the finding out the value of the a and that is by again using normal probability method by using normal probability method third what we are going to get that is z -dash is equal to okay z -dash is equals to 1 .02 and here that a value will be coming out as how much that we are going to calculate five added with 0 .5 multiplied by 1 .02 because from the condition itself okay from here we are calculating and okay so a value will be coming out as how much that is 5 .51 okay after calculating you will get how much that is 5 .51 so the second according to the second condition the value of the a is 5 .51 after that we are going with the third condition and the third condition itself is given here let us look there okay let us see there what it is so the probability of one second yeah so the probability of minus a to a and that value is 0 .8 4 4 4 .4.

04:50 Okay.

04:51 And now to change this condition we have we should multiply with 2...

Question

Assuming a random variable, x, has a normal distribution with ? = 5 and ? = 0.5, find the value of "a" for: a) P(0<x<a) = 0.1772, b) P(a<x) = 0.1539, c) P(-a<x<a) = 0.8444.

Question

Assuming a random variable, x, has a normal distribution with ? = 5 and ? = 0.5, find the value of "a" for: a) P(0<x<a) = 0.1772, b) P(a<x) = 0.1539, c) P(-a<x<a) = 0.8444.

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