7. Using tables to calculate probabilities from the normal...

7. Using tables to calculate probabilities from the normal distribution Use the following unit normal tables and accompanying figures to determine the probability that a z-score value would fall within each of the specified ranges. To use the tables, click on the Unit Normal Tables tab beneath the figures, and use the dropdown box to select the desired range of z-score values. A table of the proportions of the normal distribution corresponding to that range of z-scores will appear. If you need a different range of z-scores, simply click on the box again and select a new range. Suggestion: For each of the following five questions, make a sketch of the area under the normal distribution you are seeking. This sketch will help you determine which column(s) of the unit normal tables to use in determining the appropriate probability. 1. p(z > 2.5) = 2. p(z > -2.6) = 3. p(z < 1.3) = 4. p(1.6 < z < 2.6) = 5. p(-3.2 < z < 1.2) = Body B Tail C D: Between 0 and z Unit Normal Tables

Transcript

00:01 There is given a z value here.

00:04 If there's a z value, we have to just be sure about that.

00:09 This is the standard normal distribution.

00:11 So for standard normal distribution, the mean value, which is denoted by mu, that should be zero.

00:16 And the standard deviation, which is denoted by sigma, that should be one here.

00:21 So i can define the random variable to z, which is normal that is derivative.

00:25 That is zero and one.

00:27 Great.

00:28 So the first one.

00:30 The probability of z is greater than 2 .5.

00:33 So first of all, let me just graph this one and find the area.

00:37 This is the normal distribution here.

00:39 So the mean value, which is zero.

00:42 And this is the z value is equal to 2 .5.

00:45 So we have to get the area of this region here, this shaded region.

00:49 So how can i just find the value? if you are using the grap calculator, you can use the normal cdf function here.

00:55 Then we'll look at the shaded region, the initial or the lower boundary.

00:59 Is 2 .5 and the shaded region that goes to positive infinity so i'm going to put where big number here the mean value is zero and the standard division is one let's get the answer just press second and the solution there is normal cdf here lower boundary 2 .5 the upper boundary is one this is second e99 and the mean value is zero standard division is one let's get the probability here which is 0 .0062.

01:28 Great.

01:30 Okay, the next one, which is the probability of z is greater than, so the probability of z, which is greater than negative 2 .6.

01:41 Let me just graph the normal distribution again.

01:45 Here is the z value or the main value is zero, and there is negative 2 .6 here.

01:50 So we have to get the area of the region, which is greater than negative 2 .6.

01:56 This shaded region is of the wanted area in this question.

02:01 So to get the area of this one, again, i'm going to use the normal cdf.

02:06 So for shaded region, the minimum value is, or the lower boundary, negative 2 .6.

02:12 There is no in upper boundary.

02:13 Again, that goes to infinity.

02:15 And the mean value, which is zero, and the standard division is one.

02:20 Let's get the answer.

02:22 Second distribution, there is normal cdf here.

02:25 Negative 2 .6 and this is 1 second e99 and this is 0 and 1 we have here which is equal to this is 0 .999 and 5 3.

02:40 Okay and the next one which is less than 1 .3 so the probability of z which is less than 1 .3 so what that means? let me just graph it again.

02:56 Here is the mean value is zero and there is z is equal to 1 .3 here so we have to get the aria for this region here let me just use the blue one this is the shaded region that we need to find for this question again i'm going to use the normal cdf function here when we look at the value the lower boundary that goes to negative infinity so i'm going to put a very small number here the upper boundary is 1 .3 the mean value is your standard division is 1 .1 .5.

03:23 The mean value is your standard division is 1.

03:25 Let's get the answer to the second distribution normal cdf.

03:29 Negative 1, this is 2nd e99...

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