Texts let z1 be a z score that is unknown but identifiable...

Texts: Let 𝑧₁ be a 𝑧-score that is unknown but identifiable by position and area. If the symmetrical area between −𝑧₁ and +𝑧₁ is 0.9544, the value of 𝑧₁ is 2.03. A random variable 𝑋 is normally distributed with a mean of 150 and a variance of 36. Given that 𝑋=120, its corresponding 𝑧-score is -5.0.

Transcript

00:01 Probability that z is greater than are equal to 1 .15 is basically 1 minus probability that z is less than equal to 1 .15 that is 1 minus 5 of 1 .15 where 5 of x is the cdial of the standard normal distribution and that can be found out from this table so 1 .15 i can right 1 .15 as 1 .1 plus 0 .05.

00:43 So go to 1 .1 so this is 1 .1 row and go to 0 .05 column.

00:49 So where is the matching? so it will be 0 .8749.

00:56 So 1 minus 0 .8749.

01:00 So what is the value of 1 minus 0 .8749? it is 0 .1251.

01:09 So answer is 0 .8749.

01:10 So answer is 0 .159.

01:10 1 to 51.

01:12 So this is the answer for this question.

01:17 The next question is probability that minus 1 .78 less than it equal to z less than it equal to 0 .35.

01:25 This is actually the formula cdf evaluated at 0 .35 minus cdf evaluated at negative 1 .78.

01:32 And there is a very important formula cdf of negative x is 1 minus cdf evaluated at x.

01:38 So that means it is by of 0 .35 minus of 1 minus 5.

01:43 1 .78 so that means it is 5 of 0 .35 plus 5 of 1 .78 minus 1 so let's plug in the values 0 .35 so go back to the table 0 .35 means 0 .05 and 0 .05 so 0 .66 .6 6368 and how about 1 .78 1 .78 is 1 .7 and 0 .08 column so 1 .7 and 0 .08 column so 1 .7 and 0 .08 90 .08 is this .9625.

02:18 So 0 .9625 .0638.

02:22 0 .6368 plus .9625 minus 1...

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