let z denote a random variable having a normal distribution with 0 and 1 determine each of the f

Step 1: For part a, we want to find the probability that (0.50 < z < 0.86). By symmetry, this

Let z denote a random variable having a normal distribution...

Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the following probabilities. (You may need to use a table. Round your answers to four decimal places.) a. P(0.50 < z < 0.86) b. P(-0.86 < z < -0.5) c. P(-0.5 < z < 0.86) d. P(z > -1.24) e. P(z < 1.40 or z > 2.60)

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Now let me bring up your question here.

00:06 In this question we want to use the z table to compute the falling probabilities.

00:13 So let me copy the z table for you.

00:16 And i will show you how to use the z table here.

00:21 Now let me put the table down here for you.

00:26 And now notice that the table i bring up here, it has the area on the left tail.

00:32 And therefore the z score on the left tail.

00:34 With the negative value here.

00:37 Now we have the question a.

00:40 I want to find the probability that z it will be between 0 .5 and 0 .86.

00:51 Here because this z here on the right tail, so we want to convert this on to the left tail because of the symmetry it will also equal to the z with between the minus 0 .86 and the minus 0 .5.

01:10 And then this one will equal to the probability of the z smaller than minus 0 .5 minus the z smaller than minus 0 .86.

01:23 For this one we see minus 0 .5, we see it will be this one.

01:29 So the corresponding probability equals to 0 .385 minus.

01:36 For this one, we have a minus 0 .85.

01:36 For this one, we have a minus 0 .8.

01:40 6th so therefore the corresponding probability equal to 0 .1 49 and it will compute it we get equal to 0 .385 minus 0 .1949 equal to the 0 .116 this will be the answer for the a...

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