C find the probabilities for each using the standard normal...

C. Find the probabilities for each, using the standard normal distribution. a). P(0 < z < 1.69) = _________ b). P(-2.46 < z < 1.74) = ___________ D. Find the standard z-score value below: a). 53.98% of the area under the distribution curve lies to the left of z. ___________ b). 82.12% of the area under the distribution curve lies to the right of z. ____________ c). Find the two z-scores so that 44% of the middle area is bounded by them_______ E. Find the area under the standard normal distribution curve for the problems a) To the right of z = 1.10 b) Between z = -1.12 and z = 0.24 c) To the left of z = 2.11

Transcript

00:01 Alright, in your question you have many z -score values that we are to look up and find the areas between or left or right of them.

00:09 So let's take a quick look at how a z -table works.

00:12 This is a z -table and the probability or the z's that are listed, what we see down in the field in this area, are areas to the left of z.

00:25 So we have to adjust based on what we're looking for.

00:28 If we want left, it's easy because the numbers are directly in the table.

00:34 But if it's to the right or between things, then we have to do some subtraction along with it.

00:40 Alright, so let's get started.

00:43 The first one we want to look for is you want the probability of being between 0 and 1 .69.

00:54 So i'm going to find 1 .69.

00:57 There's 1 .6.

01:00 There's 9, which works out to .9545.

01:05 And because we're working with a between situation, i take the larger z -score, .94, i'm sorry, .9545, and i subtract the lower z -score.

01:24 But a 0 we should know.

01:25 0 is just 50 % or right in the middle.

01:28 So i'm going to subtract .5, which works out to 0 .4545.

01:34 Now the next one i want to find, again, always find when we're looking between, find the larger one first and then subtract the z for the lower score.

01:45 Okay, so 1 .74 is the next one.

01:49 There's 1 .7.

01:50 And here comes down the 4 column, .9591.

01:55 .9591 minus, and now i'm going to find this negative 2 .46 on a negative z table.

02:07 There's negative 2.

02:08 6 will be right here, .0069, and subtract those two.

02:21 And after that, we're going to jump down to e and keep working because they're similar questions.

02:28 We'll do d last.

02:30 All right, so this one works out to 0 .9522.

02:34 All right, i want to go right of z equals 1.

02:40 So when i look at a z table here, let's erase the old ones.

02:45 Z equals 1, right there, 1 .00, .8413.