I what does a z score measure ii what does standardizing a...

Name: i what does a z score measure ii what does standardizing a normal distribution do to the mean iii is x sim n01 a standardized normal distribution why or why not iv what is the z score of x 1 14441
Uploaded: 2022-07-18T18:56:11-08:00
Duration: 6 min 18 s
Channel: Steve Galvin
Description: i what does a z score measure ii what does standardizing a normal distribution do to the mean iii is x sim n01 a standardized normal distribution why or why not iv what is the z score of x 1 14441

(i) What does a z-score measure? (ii) What does standardizing a normal distribution do to the mean? (iii) Is $X \sim N(0,1)$ a standardized normal distribution? Why or why not? (iv) What is the z-score of $x = 12$, if it is two standard deviations to the right of the mean? (v) What is the z-score of $x = 9$, if it is 1.5 standard deviations to the left of the mean? (vi) What is the z-score of $x = -2$, if it is 2.78 standard deviations to the right of the mean? (vii) What is the z-score of $x = 7$, if it is 0.133 standard deviations to the left of the mean?

Transcript

00:01 All right.

00:01 So first off, i want to start off by reminding you what the definition of a z score is.

00:08 A z score is the number of standard deviations that a given value is from the mean.

00:15 And if that number is to the right of the mean, then the z score is a positive number.

00:21 And if that number is to the left of the mean, then it has a negative z score.

00:27 So let's look at part a.

00:30 What is this? the z score of x equals 4 if it is 1 .9 standard deviations to the left of the meet.

00:40 That means that x equals 4 has a z score of negative 1 .9.

00:51 See right there it just says is 1 .9 standard deviations to the left of the mean.

00:57 That's the definition of z score.

00:59 In other words the z score is 1 .9 with a negative.

01:03 Since it's to the left of the mean.

01:06 Part b, what is the z score of x equals 5 if it is 0 .166 standard deviations to the left of the mean? okay, to the left of the mean, so it's negative.

01:21 And if it's 0 .166 standard deviations to the left, then your answer is z equals negative .166.

01:32 Okay, part c, if x is in a normal distribution with a 12 and a 1 in parentheses.

01:43 Well, here's what you need to know.

01:45 The first number after the n is the mean, and the second number is the standard deviation.

01:55 So now, part c says if a value in this distribution has a z score of negative 2 .25, what was that number? so here's what we're going to do.

02:09 We have our z score formula.

02:11 Z equals score minus mean divided by standard deviation.

02:18 So here in this problem, z is negative 2 .25.

02:27 So i'm going to substitute that there.

02:30 Equals the score is unknown minus the mean of 12 divided by the standard deviation of 1.

02:38 Now, isn't that really just negative 2 .25 equals x minus 12? and then if you add 12 to both sides, we will get that x is, well, i've got to grab my calculator here...

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