12.7 approximately normal in shape?

Name: Problem 7, Chapter 12: Statistics Learning From Data
Uploaded: 2023-09-01T00:59:34-08:00
Duration: 3 min 47 s
Channel: Marcella Sippey
Description: 12.7 approximately normal in shape?

Key Concepts

Skewness

Skewness measures the degree to which a probability distribution leans to one side. A symmetric distribution has a skewness of zero, whereas a distribution that is not symmetric will have positive or negative skewness. An approximately normal distribution should have minimal skewness, indicating that the data does not lean heavily towards one end.

Kurtosis

Kurtosis refers to the shape of the tails of a distribution and its peakedness. A normal distribution has a specific kurtosis value (mesokurtic), and any significant deviation from this value indicates that the distribution may have more pronounced tails (leptokurtic) or flatter tails (platykurtic), affecting the overall shape.

Normal Distribution

The normal distribution is a fundamental probability distribution in statistics that is characterized by its bell-shaped curve. It is defined by its mean and standard deviation, and many phenomena in nature and measurement errors tend to follow this distribution. Its symmetry about the mean makes it a cornerstone concept in inferential statistics.

Symmetry

Symmetry in a distribution means that the left and right sides of the distribution mirror each other around a central point, usually the mean. In the context of the normal distribution, symmetry ensures that approximately equal proportions of values fall on either side of the mean, contributing to its bell-shaped form.

Transcript

00:01 All right, according to some medical advisors, a body mass index, bmi, between 19 and 25 suggests a healthful weight.

00:08 So they wanted to use this formula, bmi equals 704 times your weight in pounds.

00:15 I'm just going to call that w over your height in inches squared.

00:19 So over h squared to find the weight range w to the nearest pound that gives a healthful bmi for each height.

00:27 All right, so they're going to give us a height.

00:29 So i'm going to solve for w.

00:31 So i'm going to take that bmi times h squared, and that's going to equal 704 w.

00:41 So if i want to find the weight at that certain height, i need that bmi times h squared divided by 704.

00:50 So now i'm going to use this formula right here.

00:54 I'm going to circle it here.

00:55 And we have to figure out for the 19 to 25 range, right, for that bmi at each specific height.

01:03 So the first equation here, i want the bmi to be 19, and i want my height to be 72.

01:12 And i'm going to divide that by 704, and that'll give me the weight.

01:17 So 19 times 72 squared, and then i'm going to divide that by 704, and that'll give me a number of 139 .9.

01:30 And they ask you to do it to the nearest pound.

01:33 So that's going to be 139 .9 will round to 140 pounds.

01:39 Then i'm going to take this upper level of the bmi at 25 for the exact same height and square it, divide it by 704, and set that equal to w.

01:50 Punch that in the calculator again.

01:53 And then you're going to find out that that comes out to be, let's see, a couple more, 184 .09...

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