AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all...

29
AP Statistics: Section 2.2 B

TAGS:

Transcript of AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all...

Page 1: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

AP Statistics: Section 2.2 B

Page 2: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

The Standard Normal Distribution

As the 68-95-99.7 Rule suggests, all Normal distributions share many common

properties. In fact, all Normal distributions are the same if we measure in units of size

with the mean as center.

Page 3: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

Changing to these units requires us

to standardize: z = , as

we did in section 2.1.

x

Page 4: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

If the variable we standardize has a Normal distribution, then so does

the new variable z. This is true because standardizing is a linear

transformation and does not change the shape of a distribution. This new distribution is called the

Standard Normal distribution.

Page 5: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

The notation for the standard Normal distribution is ______.)1,0(N

Page 6: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

The standard Normal distribution is a density curve. Any question about the proportion of observations can

be answered by finding the area under the curve. Because all Normal distributions are the same when we

standardize, we can find areas under any Normal curve from a

table (or calculator).

Page 7: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

Turn to Table A in the front of your text.

Page 8: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.
Page 9: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.
Page 10: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

0934.9066.1

Page 11: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

Calculator:2nd VARS (DISTR)2:normalcdf(ENTERnormalcdf(lower limit, upper limit)

normalcdf(1.32, 10000)

0934.

Page 12: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.
Page 13: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.
Page 14: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

5570.2843.8413.

Page 15: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

normalcdf(-.57, 1)

5570.

Page 16: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

Normal Distribution Calculations

We can answer any question about proportions of observations in a

Normal distribution by ____________ and then using the

Standard Normal table. standardizing

Page 17: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

Here is a recipe to do so.

1. State the problem in terms of the observed variable x. Draw a picture of the distribution and

_____the area of interest under the curve.2. Standardize x to restate the problem in terms of a standard Normal variable z. 3. Use the table or calculator and find the required area under the standard Normal curve.4. Write your conclusion in the context of the problem.

find

Page 18: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

33.230

170240

z

0099.9901.1

0.99% of all 14-year old boys have a cholesterol level of more than 240 mg/dl

Page 19: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

Calculator:

normalcdf(240,10000,

normalcdf(240, 10000, 170, 30)

),

0098.

Page 20: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

67.30

170150

z 67.

30

170190

z

4972.2514.7486. 49.7 % of 14-year old boys have blood cholesterol between 150 & 190 mg/dl

Page 21: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

Calculator:

normalcdf(150,190,170,30)

4950.

Page 22: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.
Page 23: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.
Page 24: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

67.

30

17067.

x

9.149x

25% of 14-year old boys have blood cholesterol levels less than 149.9mg/dl

Page 25: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

Calculator:2nd VARS (DISTR)3: invNorm(ENTERinvNorm(area to left,

invNorm(.25, 170, 30)

),

765.149x

Page 26: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.
Page 27: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.
Page 28: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

84.

30

17084.

x

2.195x

80% of 14-year old boys have blood cholesterol levels less than 195.2

Page 29: AP Statistics: Section 2.2 B. The Standard Normal Distribution As the 68-95-99.7 Rule suggests, all Normal distributions share many common properties.

invNorm(.8, 170, 30)

249.195x


ILLINOIS INTEGRATED WATER QUALITY REPORT AND …...74,709 74,536 90.1 93.0 9.9 7.0 0.0 0.0 0.2 0.2 0.0 0.0 Secondary Contact(2) 318,477 1,092 100 100.0 -- -- -- -- 99.7 99.7 0.0 0.0

ILLINOIS INTEGRATED WATER QUALITY REPORT AND …...74,709 74,536 90.1 93.0 9.9 7.0 0.0 0.0 0.2 0.2 0.0 0.0 Secondary Contact(2) 318,477 1,092 100 100.0 -- -- -- -- 99.7 99.7 0.0 0.0

And the 68-95-99.7 Rule THE NORMAL DISTRIBUTION. SKEWED DISTRIBUTIONS & OUTLIERS.

And the 68-95-99.7 Rule THE NORMAL DISTRIBUTION. SKEWED DISTRIBUTIONS & OUTLIERS.

The Normal Distribution - USP · 9.2 The Normal Distribution The 68–95–99.7 Rule is useful in describing how unusual a z-score is. But often in business we want a more precise

The Normal Distribution - USP · 9.2 The Normal Distribution The 68–95–99.7 Rule is useful in describing how unusual a z-score is. But often in business we want a more precise

HMEC Glossary - Federal Highway Administration · HMEC Glossary 1 . 68-95-99.7 Rule: The values that represent what percentage of a population will fit in a normal distribution depending

HMEC Glossary - Federal Highway Administration · HMEC Glossary 1 . 68-95-99.7 Rule: The values that represent what percentage of a population will fit in a normal distribution depending

2020 DRAFT EU BUDGET - European Commission · 2019-06-05 · Voted budget execution (in EUR million) 100% 100% 100% % EXECUTED COMMITMENTS % EXECUTED PAYMENTS 99.7% 99.7% 586.2 99.68%

2020 DRAFT EU BUDGET - European Commission · 2019-06-05 · Voted budget execution (in EUR million) 100% 100% 100% % EXECUTED COMMITMENTS % EXECUTED PAYMENTS 99.7% 99.7% 586.2 99.68%

Reinforcing the 68-95-99.7 Rule

Reinforcing the 68-95-99.7 Rule

Normal Gallbladder Ejection Fraction in Normal Thai ... · PDF filebiliary colic symptoms without cholelithiasis, and suggests the potential of chronic inflammation(1-3). ... in healthy

Normal Gallbladder Ejection Fraction in Normal Thai ... · PDF filebiliary colic symptoms without cholelithiasis, and suggests the potential of chronic inflammation(1-3). ... in healthy

The empirical (68-95-99.7) rulefisher.utstat.toronto.edu/~hadas/STA220/Lecture notes... · 2007-09-23 · week3 1 The empirical (68-95-99.7) rule • With a bell shaped distribution,

The empirical (68-95-99.7) rulefisher.utstat.toronto.edu/~hadas/STA220/Lecture notes... · 2007-09-23 · week3 1 The empirical (68-95-99.7) rule • With a bell shaped distribution,

Density Curves and Normal Distributions density curve. · The normal distribution follows an important rule called the 68-95-99.7% rule. It states that in any normal distribution,

Density Curves and Normal Distributions density curve. · The normal distribution follows an important rule called the 68-95-99.7% rule. It states that in any normal distribution,

Objectives (BPS 3) The Normal distributions Density curves Normal distributions The 68-95-99.7 rule The standard Normal distribution Finding.

Objectives (BPS 3) The Normal distributions Density curves Normal distributions The 68-95-99.7 rule The standard Normal distribution Finding.

Maine.gov · Web viewGoal to be at 100% by end of fiscal training year 2011 on June 30th. Last Fiscal Year (2010) at 99.7% 381 of 382 have completed annual NAPPI training 99.7% 100

Maine.gov · Web viewGoal to be at 100% by end of fiscal training year 2011 on June 30th. Last Fiscal Year (2010) at 99.7% 381 of 382 have completed annual NAPPI training 99.7% 100

1 Balboa (B/.) = 99.7 Yen (JPY) · Exchange Rate (October 2013) 1 Balboa (B/.) = 99.7 Yen (JPY) 1 Yen = 0.01003 Balboa 1 US Dollar (US$) = 99.7 Yen 1 US$ = 1 Balboa

1 Balboa (B/.) = 99.7 Yen (JPY) · Exchange Rate (October 2013) 1 Balboa (B/.) = 99.7 Yen (JPY) 1 Yen = 0.01003 Balboa 1 US Dollar (US$) = 99.7 Yen 1 US$ = 1 Balboa

10 ways to Protect Your pMDI Product · 100.3 99.7 100.5 Stored Horizontal 101.2 99.7 100.6 Patients who use their inhalers on an as-needed basis may improve compliance through pMDIs

10 ways to Protect Your pMDI Product · 100.3 99.7 100.5 Stored Horizontal 101.2 99.7 100.6 Patients who use their inhalers on an as-needed basis may improve compliance through pMDIs

A.I.A. Suggests

A.I.A. Suggests

1 The Sample Mean. 2 68 - 95 - 99.7 rule Recall we learned a variable could have a normal distribution? This was useful because then we could say approximately.

1 The Sample Mean. 2 68 - 95 - 99.7 rule Recall we learned a variable could have a normal distribution? This was useful because then we could say approximately.

Normal Distribution · Web viewReview the properties of normal curves and the empirical or 68-95-99.7 rule related to how data is positioned in a normal distribution. Then, distribute

Normal Distribution · Web viewReview the properties of normal curves and the empirical or 68-95-99.7 rule related to how data is positioned in a normal distribution. Then, distribute

(SPEC) Glycerin, Vegetable 99.7% … USP/Kosher OTHGLYPALMUSPKMY746 ... Conforms to USP 36 Residue on Ignition (USP 36): ... (SPEC) Glycerin, Vegetable 99.7% OTHGLYPALMUSPKMY746

(SPEC) Glycerin, Vegetable 99.7% … USP/Kosher OTHGLYPALMUSPKMY746 ... Conforms to USP 36 Residue on Ignition (USP 36): ... (SPEC) Glycerin, Vegetable 99.7% OTHGLYPALMUSPKMY746

Zinc Oxide (99.7%) by Upper India Smelting And Refinery Works Yamunanagar

Zinc Oxide (99.7%) by Upper India Smelting And Refinery Works Yamunanagar

Balance - Suggests

Balance - Suggests

The Normal Distributions. Density curves Normal distributions The 68-95-99.7 rule The standard normal distribution Normal distribution calculations.

The Normal Distributions. Density curves Normal distributions The 68-95-99.7 rule The standard normal distribution Normal distribution calculations.