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 probabilities below. (Round all answers to four decimal places.) (a) P(z < 0.3) = (b) P(z < -0.3) = (c) P(0.40 < z < 0.86) = (d) P(-0.86 < z < -0.40) = (e) P(-0.40 < z < 0.86) = (f) P(z > -1.25) = (g) P(z < -1.5 or z > 2.50) =

Transcript

00:01 So in this question, you need to use the normal table.

00:03 They stand a normal table because basically have a normal distribution with mean zero and i stand a deviation 1, which means that we can use the z table to find the sensors.

00:15 So in item a, we want to find the probability that z is smaller than 0 .3.

00:20 So you can use the normal table by, for example, you have here the table.

00:25 We have the values of z here.

00:27 So here, usually in the row, you're going to have the initial.

00:30 Show value, for example, if it is like 0, or if it is like 1, 1 .1.

00:37 So you're going to have the whole number, if you have any, in the first decimal place.

00:42 If you don't have any whole number, such as the case for letter a, you should pick the first row and then look at the column as well.

00:53 So the column will give us the second decimal place.

00:57 So in our case, we want the 03, because this means that this is the, in this case, the second decimal place that we have, and that's it, right? so that will be okay for us.

01:13 So in this case here, this means that now we should look at the value that i have here to find the answer.

01:20 So if you do this, you're going to find 0 .61, 79.

01:24 Okay.

01:26 Now for letter b, we have the probability that z here is smaller than negative 0 .3.

01:35 But it will be the same.

01:35 You're going to find a table that has like a minus 0, and that's okay.

01:41 And then you pick here the 0 .3, which basically means that it is minus 0 .3.

01:47 And you're going to find this using the table, equals to 038, 21.

01:53 Now, for letter c, we have two values.

01:56 We have z being between 04 and 086.

02:02 So basically, we are going to find each one individually.

02:05 We are going to first find what is the probability that z is less than the number in the right.

02:11 And then we are going to subtract this from the value given by z being less than 04.

02:17 Again, you're going to find the values here in the table corresponding to each.

02:23 One of this, so for example this is 0 .80, 51, and this is 0 .654.

02:32 So this will give us as the answer, 014, 97.

02:37 Now for letter d, we have like almost the same thing, but it's like a minus 86 and minus 4...

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