...C H A P T E R 6 The Normal Distribution Objectives After completing this chapter, you should be able to Outline Introduction 6–1 Normal Distributions 1 2 3 4 5 6 7 Identify distributions as symmetric or skewed. Identify the properties of a normal distribution. Find the area under the standard normal distribution, given various z values. Find probabilities for a normally distributed variable by transforming it into a standard normal variable. Find specific data values for given percentages, using the standard normal distribution. Use the central limit theorem to solve problems involving sample means for large samples. Use the normal approximation to compute probabilities for a binomial variable. 6–2 Applications of the Normal Distribution 6–3 The Central Limit Theorem 6–4 The Normal Approximation to the Binomial Distribution Summary 6–1 300 Chapter 6 The Normal Distribution Statistics Today What Is Normal? Medical researchers have determined so-called normal intervals for a person’s blood pressure, cholesterol, triglycerides, and the like. For example, the normal range of systolic blood pressure is 110 to 140. The normal interval for a person’s triglycerides is from 30 to 200 milligrams per deciliter (mg/dl). By measuring these variables, a physician can determine if a patient’s vital statistics are within the normal interval or if some type of treatment is needed to correct a condition and avoid future illnesses. The question then is,...
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...The probability distribution of the population data is called the population distribution. Tables 7.1 and 7.2 on page 309 of the text provide an example of such a distribution. The probability distribution of a sample statistic is called its sampling distribution. Tables 7.3 to 7.5 on page 311 of the text provide an example of the sampling distribution of the sample mean. 1. Sampling error is the difference between the value of the sample statistic and the value of the corresponding population parameter, assuming that the sample is random and no nonsampling error has been made. Example 7–1 on page 312 of the text exhibits sampling error. Sampling errors occur only in sample surveys. 2. Nonsampling errors are errors that may occur during collection, recording, and tabulation of data. The second part of Example 7–1 on pages 312 and 313 of the text exhibits nonsampling error. Nonsampling errors occur both in sample surveys and censuses. 3. a. [pic] b. [pic][pic] Sampling error = [pic] c. Liza’s incorrect [pic][pic] [pic] Sampling error (from part b) = –1.83 Nonsampling error [pic] d. | Sample | [pic] |[pic] | |15, 13, 8, 17 |13.25 |.92 | |15, 13, 8, 9 |11.25 |–1.08 | |15, 13, 17, 9 |13.50 |1.17 | |15, 8, 17, 9 |12...
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...Table 1: Table of the Standard Normal Cumulative Distribution Function Φ(z) z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 0.0003 0.0005 0.0007 0.0010 0.0013 0.0019 0.0026 0.0035 0.0047 0.0062 0.0082 0.0107 0.0139 0.0179 0.0228 0.0287 0.0359 0.0446 0.0548 0.0668 0.0808 0.0968 0.1151 0.1357 0.1587 0.1841 0.2119 0.2420 0.2743 0.3085 0.3446 0.3821 0.4207 0.4602 0.5000 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.9987 0.9990 0.9993 0.9995 0.9997 0.0003 0.0005 0.0007 0.0009 0.0013 0.0018 0.0025 0.0034 0.0045 0.0060 0.0080 0.0104 0.0136 0.0174 0.0222 0.0281 0.0351 0.0436 0.0537 0.0655 0.0793 0.0951 0.1131 0.1335 0.1562 0.1814 0.2090 0.2389 0.2709 0.3050 0.3409 0.3783 0.4168 0.4562 0.4960 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7611 0.7910 0.8186 0.8438 0.8665 0.8869 0.9049 ...
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...Mercedes and BMW have been competing head-to-head for market share in the luxury-car market for more than four decades. Back in 1959, BMW (Bayerische Motoren Werke) almost went bankrupt and nearly sold out to Daimler-Benz, the maker of Mercedes-Benz cars. BMW was able to recover to the point that in 1992 it passed Mercedes in worldwide sales. Among the reasons for BMWs success was its ability to sell models that were more luxurious than previous models but still focused on consumer quality and environmental responsibility. In particular, BMW targeted its sales pitch to the younger market, whereas Mercedes retained a more mature customer base. In response to BMWs success, Mercedes has been trying to change their image by launching several products in an effort to attract younger buyers who are interested in sporty, performance-oriented cars. BMW, influenced by Mercedes, is pushing for more refinement and comfort. In fact, one automotive expert says that Mercedes wants to become BMW, and vice versa. However, according to one recent automotive expert, the focus is still on luxury and comfort for Mercedes while BMW focuses on performance and driving dynamics. Even though each company produces many different models, two relatively comparable coupe automobiles are the BMW 3 Series Coupe 335i and the Mercedes CLK350 Coupe. In a recent year, the national U.S. market price for the BMW 3 Series Coupe 335i was $39,368 and for the Mercedes CLK350 Coupe was $44,520. Gas mileage for both...
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...APPENDIX, T ABLE 2: STANDARD NORMAL DISTRIBUTION TABLE ~ • The eDtries lD this bible g in the areas uDder the IblDdard Dormal c ane from 0 t o:. 0 H, : 0.0 .00 .01 .02 .03 .04 .05 .06 .0000 .0040 .0080 .0120 .0160 .0199 0.1 0.2 0.3 0.4 0.5 .0398 .0793 .1179 .1554 .19lS .0438 .0832 .1217 .1591 .1950 .0478 .0871 .1255 .1628 .1985 .0517 .0910 .1293 .1664 .0557 .0948 .1331 .1700 .2054 0.6 0.7 0.8 0.9 1.0 .2257 .2580 .2881 .3159 .3413 .2291 .2611 .2910 .3186 .3438 .2324 .2642 .2939 .3212 .3461 .2357 .2673 .2967 .3238 .3485 .2389 .2704 1.I 1.2 1.3 1.4 1.5 .3643 .3849 .4032 .4192 .4332 .3665 .3869 .4049 .4207 .4345 .3686 .3888 .3729 .3925 .4222 .4357 .3708 .3907 .4082' .4236 .4370 1.6 1.7 1.8 1.9 2.0 .4452 .4554 .4641 .4713 .4772 .4463 .4564 .4649 .4719 .4778 .4474 .4S73 .4656 .4726 .4783 .4484 2.1 2.2 2.3 2.4 2.5 .4821 .4861 .4893 .4918 .4938 .4826 2.6 2.7 2.8 2.9 3.0 .4953 .4965 .4974 .4981 .4 7 .08 .09 .0239 .07 .0279 .0319 .03S9 .0596 .0987 .1368 .1736 .2088 .0636 .1026 .1406 .1772 .2123 .0675 .1064 .1443 .1808 .2157 .0714 .1103 .1480 .1844 .2190 .07S3 .1141 . ISI7 .1879 .2224 .2422 .27}4 .3023 .3289 .3531 .2454 .2764 .3051 .3315 .3554 .2486 .2794 .3078 .3340 .3577 ...
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...City Cents City Cents 1 Vancouver, BC 5.83 15 Edmonton, AB 10.12 2 Saskatoon, SK 6.77 16 Calgary, AB 15.32 3 Abbotsford, BC 6.32 17 Oshawa, ON 6.23 4 St. John's, NL 9.68 18 Halifax, NS 8.36 5 Winnipeg, MB 5.41 19 Moncton, NB 8.83 6 Sudbury, ON 5.83 20 Price George, AB 6.19 7 Ottawa, ON 8.08 21 Brantford, ON 6.65 8 Sherbrooke, QC 6.56 22 St-Jean, QC 5.25 9 Quebec, QC 5.74 23 Regina, SK 7.23 10 Whitehorse, YT 6.06 24 Montreal, QC 6.74 11 Toronto, ON 8.62 25 Yellowknife, NWT 6.43 12 Saguenay, QC 6.20 26 Kewlowna, BC 6.83 13 Hamilton, ON 6.91 27 Windsor, ON 6.69 14 Charlottetown, PE 10.60 28 Thunder Bay, ON 6.12 1. Determining the mean, variance and standard deviation of the provided sample: Mean: 7.3429 Variance: 4.4322 Standard Deviation: 2.1053 The mean, variance, and standard deviation for electricity prices of this sample is 7.3429, 4.4322 & 2.1053 cents respectively. 2. 95% confidence interval for the mean of the population utility rates: Confidence Interval: 0.77979 We're 95% confident that the true mean falls somewhere between 6.5631and 8.1227. 3. 90% confidence interval for the mean of the population utility rates, asssuming population standard deviation 2.09 Confidence Interval: 0.6497 ...
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...Normal is defined by Oxford dictionary as conforming to a standard; usual, typical, or expected. Growing up, normal for me was constant doctor visits, medication, and unanswered questions. Twinned with the normal occurrences as a child, there were the constant feelings of anger, hate, confusion, and fear. Anger for always wanting to do what every other kid in America could, like eat ice cream. Hate for whoever in the world that had the control that made me like I was. Confusion for the constant unanswered questions. Fear for the impending unknown of what my life was going to be. I never knew what the day was going to bring. It was constantly "No you can't have that" "You're just different." Having constant health issues, life was an obstacle...
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...4/27/2014 MA3110 Statistics Otis Jackson Unit 4 problem set 1: Normal Probability Distributions Page.285 Ex 6,8,10,12 6. x = 80, z=80-10015 = -1.33 z= 0.0918 1-0.0918 = 0.9082 8. x = 110, z=110-10015 = 0.67 z= 0.7486 z= 75-10015 = -1.67 z= 0.0475 0.7486-0.0475= 0.7011 (shaded area) 10. z= 0.84 (shaded) z= -0.84 x= 100+(-0.84∙15) = 87 (rounded) 12. . z= 2.33 x= 100+(2.33∙15) = 135 (rounded) Page 288 Ex 34 34.Appendix B Data Set: Duration of Shuttle Flights a. Find the mean and standard deviation, and verify that the data have a distribution that is roughly normal. Mean= 25317115 = 220.15 Standard Deviation=115253172-(25317)2115(115-1) = 86 (rounded) The normal distribution is 115 b. Treat the statistics from part (a) as if they are population parameters and assume a normal distribution to find the values of the quartiles 1,2 and 3. Mean= 220.15 Standard Deviation= 86 Q1 = 220.5 + (-0.67 ∙ 86)= 162.53 Q2= 220.5 + (0.00 ∙ 86) = 220.5 Q3=220.5 + (0.67 ∙ 86) = 277.77 Page.300 Ex 20 Quality Control: Sampling Distribution of Proportion after constructing a new manufacturing machine. 5 prototype integrated circuit chips are produced and it is found that 2 are defective (D) and 3 are acceptable (A). Assume that two if the chips are randomly selected with replacement from this population a. After identifying the 25 different possible samples, find the proportion of defects in each of them, then use a table to describe...
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...“Normal” There is a time and place is what we are taught to think before we take action. If we are unable to do this successfully, we are thought to be a black sheep. I recognize this as I walk through the door of a 24-hour Starbucks during the middle of the night. Strangers are staying close to those who are familiar and keep to themselves, tinting a cool summer night with an uncomfortable silence similar to a library. Eyes wander; following the slightest movements of newcomers. When there is nothing to see, attention is moved elsewhere to something more unusual like the prostitute that just came in. She became pinned down by stares from those who recognized what she is. More than the standard three second stares and move on, bodies contort from where they sit. Eyebrows are raised; showing judgment of the subject that stands before them. Thoughts are running wild,” Wow so strange… I thought that the only place to see prostitutes are at random street corners… Gross… Doesn’t she know she would stand out at a place like this?... Poor thing…” Observing this, I realize that we are all so used to our own reality that, those who differ are considered unusual. She stands out against the crowd wearing all black. The cozy, romantic, lighting makes her appear as a slim silhouette among all of the random patterns and colors that surrounds her. Her face reveals an age varying from the mid to late forties, although, her body expresses an age greater than her own. The white contrasting...
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...Naniniwala ka ba sa Love? syempre sasabihin mo oo. Alam mo ba kung anong ang mga iba't ibang klase ng love? Maraming uri ng pag-ibig. May tinatawag na First love, May greatest love, May true love, At ang huli ang eternal love. kadalasan nasasaktan tayo sa first love at natututo sa greatest love. Pero kung minsan hanggang true love lang tayo. Sila yung mga taong minahal mo dahil mahal ka nila. Kumbaga, tinuruan mo yung puso mo na mahalin sila. Hindi natural na pag-ibig. Pero ang pinakaaasam ng lahat ay ang eternal love. Ito yung mahal niyo yung isa't isa. Walang nangingibabaw na pagmamahal. Dahil lahat pantay pantay. Ito yung tinatawag na soulmate o yung taong itinadhana sayo. Ikaw kilala mo na ba kung sinong nakatadhana sa’yo? Hindi naman natin malalaman e. Pero.. Minsan mapaglaro din ang tadhana. Minsan sususbukin kayo kung hanggang saan kayo tatagal. Minsan tadhana na rin ang gagawa para magkabalikan kayo. Depende lang talaga yan sa tatag ng puso niyo. Napakamapaglaro ng tadhana. Ako si Andrea Ong. 4th year high school ako nung una akong magka boyfriend. Si Mico Perez. Lihim pa nga yon sa magulang ko e. Bawal pa kasi akong mag boyfriend. Tapusin ko muna daw ang pag-aaral ko. Pero anong bawal bawal? Sa love walang pinipiling edad. Ganun naman talaga kapag nagmahal ka di ba? Sabi nga sa isang kanta. "Kapag tumibok ang puso, wala ka ng magagawa kundi sundin ito." Masarap kayang mainlove...
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...Expository Writing 101: Section EA Professor Morrone Dissociation is Normal Dissociation is when an individual mentally spaces out in order to not remember or remove themselves from a situation. The dissociation can be triggered by anything at any point in time and is often related to a traumatic experience. Individuals who dissociate intensely usually do not know that they are dissociating, and many who do seek psychiatric help. Anyone can dissociate and in her essay “When I Woke Up Tuesday Morning, It was Friday,” Martha Stout, a psychologist, speaks about her successful, ordinary, normal patients who dissociate due to traumatic experiences. Society perceives individuals who seek psychiatric assistance to be “abnormal,” but Stout challenges this concept by illustrating how her patients defy this generalization. Therapy is not just for “insane” individuals because Stout’s patients are intellectual individuals who carry through conventional lifestyles. Society labels individuals who acquire psychiatric help as irregular simply because the individuals seek the therapy. Seeking therapeutic help is the first step towards fixing personal problems that cannot be fought alone. Everyone has issues that are difficult to face on their own; in Stout’s patients’ cases, the issues are severe episodes of dissociation that hinder their everyday routines. One patient in particular, named Julia, is a successful producer of documentary films. As a child, Julia...
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...chapter 1 Health Care chapter 2 chapter 3 The World's Best fighting with Disease Saved from Certain death Selling Medicine Felix Hoffmann wanted to help his father. What followed was one of the biggest success stories in business. A doctor in a farming Community made a discovery that has saved millions of lives. Everyone expected Jeanna Giese to die, but one doctor did not give up. B write the word from Part A next to its definition 1The feeling when something hurts you. pain 2The person who controls a business or the workers manager 3 To help someone who is sick ; treat 4 A medical condition with higher than normal body temperature; fever 5. Available for sale; on the marker 6. An organization that sells goods or services to make money; Company 7. Medicine that is not liquid, you can pick it up and take it with water; pill 8. To stop something from happening; prevent 9, Almost the same; similar 10. Someone who goes to see a doctor; patient 11. 12. To make or create spmething ; produce A person who does a study to learn more about something ; researcher. A Felix Hoffmann's father was in a lot of pain, so Hoffmann did research and developed a mixture with salicylic acid. It worked well. Hoffmann told his manager at Bayer about this. The Company developed a drug called aspirin. It helped stop pain and lower fevers. They tested the new drug and found that it worked well. At first, Bayer...
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...Shawn Augustine 12-16-12 ANTHRO 101 – 2nd Take Home FINAL EXAM PART 2: Before taking this course, I thought Anthropology and anthropologists were concerned with only the study of culture and its effect on society. I later learned, Anthropology is not only limited to culture but also encompasses identity, culture, gender, race, sexuality, politics, and economics. Anthropologists do not exist to only examine cultures and say what is right and wrong in society. Their mission is to break the normalcy of theories and beliefs and prove its credibility. I found the topics of culture with respects to poverty, the power of naming, representation, and economic inequality of great interest to me because I enjoyed seeing examples of how the cultural norms we experience every day is false and misleading. We learned that culture, in an anthropological view, is a people’s way of life. These shared beliefs; food, language, work, labor, tradition, religion, art, and etiquette become bounded together into a common culture that is constantly changing. Culture veils society and when this takes place, class lines, race, gender, and segmentation occur creating a dominant culture because not everyone participates in a culture. Through transculturation, dominant culture can change existing cultures resulting in resistance causing a mix into a new culture. I previously thought poverty was not a culture but through our lesson and readings...
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...The World Bank and the International Monetary Fund will meet in Washington, D.C. Saturday and Sunday. One subject for discussion will be falling expectations for world economic growth. A new report by the I.M.F. estimates that the world economy will shrink by one and three-tenths percent this year. That would be the worst performance in more than sixty years. Three months ago, the I.M.F. predicted a small growth for this year. Major industrialized economies are expected to see the biggest decreases, shrinking by almost four percent. The I.M.F. predicts developing economies will continue to grow for the year, but only by about one and one-half percent. The I.M.F. says the world will slowly return to growth of almost two percent next year. But the lending organization warns that strong policies to supervise and support the financial system are needed if the world economy is to fully recovery. Olivier Blanchard is the chief economist for the I.M.F. He has said that banks are still in the process of rebuilding their financial positions. He added that securities markets are still operating poorly. Economic experts believe the world financial industry is moving towards recovery but with more losses to come. In all, the I.M.F. says worldwide financial losses could be as high as four trillion dollars by the end of next year. World trade is expected to drop eleven percent this year, after expanding by three percent last year. The I.M.F. report says international lending may...
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...1. Affable: (adj.) courteous and pleasant, sociable, easy to speak to 2. Aggrandize: (v.) to increase in greatness, power, or wealth; to build up or intensify; to make appear greater 3. Amorphous: (adj.) shapeless, without definite form; of no particular type or character; without organization, unity, or cohesion 4. Aura: (n.) that which surrounds (as an atmosphere); a distinctive air or personal quality 5. Contraband: (n.) illegal traffic, smuggled goods; (adj.) illegal, prohibited 6. Erudite: (adj.) scholarly, learned, bookish, pedantic 7. Gossamer: (adj.) thin, light, delicate, insubstantial; (n.) a very thin, light cloth 8. Infer: (v.) to find out by reasoning; to arrive at a conclusion on the basis of thought; to hint, suggest, imply 9. Inscrutable: (adj.) incapable of being understood; impossible to see through physically 10. Insular: (adj.) relating to, characteristic of, or situated on an island; narrow or isolated in outlook or experience 11. Irrevocable: (adj.) incapable of being changed or called back 12. Propensity: (n.) a natural inclination or predilection toward 13. Querulous: (adj.) peevish, complaining, fretful 14. Remonstrate: (v.) to argue or plead with someone against something, protest against, object to 15. Repudiate: (v.) to disown, reject, or deny the validity of | WOWs Week 11 - 1.inadvertent - (adj.) resulting from or marked by lack of attention; unintentional, accidental 2.nominal - (adj.) existing in name only, not real; too small...
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