Consider a normal distribution curve where the middle 30 of...

Consider a normal distribution curve where the middle 30 % of the area under the curve lies above the interval ( 4 , 15 ). Use this information to find the mean, μ , and the standard deviation, σ , of the distribution.

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00:01 In this question, when given a normal distribution curve, when the middle 30 % of the area under the curve, lies in this interval 4 to 15.

00:12 So i'm going to draw the normal distribution.

00:17 So suppose it x following the normal distribution with the mean, mu, and variance sigma square, where sigma is the standard deviation.

00:29 So here is the mean, mu.

00:35 And the 30 % of the area on the curve, the middle 30%, so that would be this over here.

00:45 And so this would be 30 % or 0 .3 in the area.

00:53 So in this spot, this is 4 and here will be 15.

01:01 Now, we want to find the mean mu and the standard deviation sigma.

01:08 We cannot key this into the calculator because the mean mu is unknown.

01:14 So what we need to do is to shift the normal distribution graph is to normalize it.

01:23 So into standard normal graph.

01:27 Standard normal graph, the mean is zero.

01:30 And so in this case, how are we going to change it to the standard normal? so let's form the probability statement for this.

01:44 Area under graph is probability.

01:46 So i'm going to let x be the normal distribution.

01:53 Where the mean is mu and variance is sigma square.

01:59 So probability of x between 4 and 15 is the area which is 30 % or 0 .3 in decimal.

02:11 So i'm going to apply x minus mu on all sides...

Question

Consider a normal distribution curve where the middle 30 % of the area under the curve lies above the interval ( 4 , 15 ). Use this information to find the mean, μ , and the standard deviation, σ , of the distribution.

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