(1 point) Suppose that X is normally distributed with mean...

(1 point) Suppose that X is normally distributed with mean 80 and standard deviation 23. A. What is the probability that X is greater than 115.88? Probability = B. What value of X does only the top 18% exceed? X =

Transcript

00:01 Hello students we are going to write here normal distribution is given with mean and standard evaluation.

00:06 So in the first case we are going to find probability in the second case we are going to find the value of x that does only the top 18 % exceed.

00:16 So basically if i write here for this in the normal distribution if i write here in the normal distribution all the random variables are all the random variables are distributed amongst bell shaped curve so this must be erased something like this all the random variables are distributed something like this z and minus z and probability of p j right -hand side area is 0 .5 left -hand side area is 0 .5 it means that total area under normal distribution curve is 1 so we are going to write here for for this this must be j score attribute is x minus mu divided by sigma so in the first case what is the probability that the random variable of x is greater than this so it means that z score attribute is x minus so 115 .88 minus we are going to write here this must be 80 divided by two three so if i right here for this this must be written as 115 .88 minus 80 that is 35 .88 and this must be divided by we are going to write here this must be divided by two three which is equivalent to this must be divided by two three which is equivalent to 1 .56 we need that probability of jad values greater than particular z score which is 1 .56 so we need that particular area we need that particular area which is one minus probability of z value is less than equivalent to 1 .56 so we are going to write here for this so if i write here for this 1 minus 0 .94062 that is equivalent to 0 .0 594 so in the first case this is our probability value hence probability is 0594 0594 in the second case we are going to write here in the second case the value of x does not only top percent top 18 percent exceed so if i write here so if i write here for this we need to find x does only top 18 % exceed.

03:08 So probability of z value is greater than particular z score that is equivalent to 18%.

03:14 It means that 0 .18.

03:16 This must be 0 .18 probability of z value.

03:22 So this must be written as probability of z value is less than equivalent to z score which is 1 minus probability of z value is greater than particular z score which is 1 minus 0 .18 that is equivalent to 0 .82 that is equivalent to 0 .82 which is z score attribute as 0 .92 so if i write here for this this is x minus mu divided by sigma so x value as we are going to write here 0 .92 0 .92 multiplied by sigma...

Question

(1 point) Suppose that X is normally distributed with mean 80 and standard deviation 23. A. What is the probability that X is greater than 115.88? Probability = B. What value of X does only the top 18% exceed? X =

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