1. (Standard normal distribution) Let Z be a standard normal...

1. (Standard normal distribution) Let Z be a standard normal random variable. Use this information and the z-table to answer the following questions a-g. a. By which color is the probability P( Z > 2.0) represented on the given bell curve below. b. Find P( Z ? -0.19) c. Find P( 0 ? Z ? 1.5) and P( -1.5 ? Z ? 0) d. Find P( Z > 1.7). e. Find c such that P( Z ? c) ? 0.2776. f. Find r such that P( Z > r) ? 0.2776. g. Find t such that P( Z < t) ? 0.8000.

Transcript

00:02 In this question part a, we have to tell that by which color is the probability z greater than 2 .0 represented on the given bell curve.

00:19 So probability z greater than 2 .0 is equal to 1 minus probability z smaller than 2 .0.

00:31 It will be equal to 1 minus 0 .9772.

00:36 Getting this from z table and it will be equal to 0 .022750.

00:45 So p.

00:46 Z greater than 2 .0 will be equal to 0 .0228.

00:53 Therefore the color is blue which is the probability z greater than 2 .0 represented on the bell curve.

01:23 Now part b we have to find p z smaller than or equal to minus 0 .19 p z smaller than or equal to minus 0 .19 will be equal to p z smaller than 0 .19 it will be equal to 1 minus p z smaller than or 0 .19 and it will be equal to 1 minus 0 .5753 finding this value by z table and we will get 0 .4246 therefore probability z smaller than or equal to minus 0 .19 is equal to 0 .426 it is the final answer of part b.

02:26 Now coming to the part c we have to find probability 0 smaller than za smaller than 1 .5 and probability 1 .5 smaller than or equal to x smaller than or equal to 0 here the solution is probability, 0 smaller than equal to z smaller than equal to 1 .5 will be equal to probability z smaller than or equal to 1 .5 minus probability z smaller than 0 from z table the value of this will be 0 .9332 and value for this will be 0 .5 so calculating we will get the value 0 .4 332 so this is the answer for r c t minus 1 .5 0 it will be equal to probability z smaller than 0 minus probability z smaller than minus 1 .5 from z table the value of this will be my 0 .5 minus and we'll take it 1 minus probability z smaller than 1 .5 0 .5 minus 1 minus 0 .9 332 this we get from z table so 0 .5 minus 0 .5 minus 0 .0 6668 so calculating we will get 0 .4332.

04:26 So this is the answer.

04:31 Now coming to the part d of the question.

04:36 Here we have to find out pz greater than 1 .7.

04:41 So probability z greater than 1 .7 will be equal to 1 minus probability z smaller than 1 .7.

04:51 Now 1 minus from z table we get value of this 0 .9554 and it will be equal to 0 .40446.

05:04 Therefore the answer will be probability z greater than 1 .7 equal to 0 .0446.

05:12 This is the answer for part d...

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