03 1450 Chapter 3 - Chapter 3 The Normal Distributions STAT 1450 3.0 The Normal Distributions Connecting Chapter 3 to our Current Knowledge of

# 03 1450 Chapter 3 - Chapter 3 The Normal Distributions STAT...

• Notes
• 194

This preview shows page 1 - 11 out of 194 pages.

Chapter 3: The Normal Distributions STAT 1450 Subscribe to view the full document.

Connecting Chapter 3 to our Current Knowledge of Statistics In Chapters 1 and 2, we explored distributions for quantitative variables by: making graphical displays of data (Chapter 1) , looking for an overall pattern and four key features ( center , spread , shape , and outliers ) (Chapters 1/2) , and calculating numerical summaries to briefly describe center, spread, and location and spread (Chapter 2) . Let’s extend this: Approximate the overall pattern of a large sample size with a smooth curve . Use this smooth curve to determine probabilities of events. 3.0 The Normal Distributions 3.1 Density Curves A density curve describes the overall pattern of a distribution. The area under the curve for a given range of values along the -axis is the proportion of the population that falls in that range. Important: the density curve has an area of exactly 1 underneath it. You might find it helpful to think about this in terms of 100%. 3.1 Density Curves Subscribe to view the full document.

Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 3.1 Density Curves Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 a. What would you expect the typical January hi temperature to be? 3.1 Density Curves Subscribe to view the full document.

Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 a. What would you expect the typical January hi temperature to be? Taking the average of the endpoints yields 37.5 degrees. 3.1 Density Curves Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 b. What proportion of the time is the January hi temperature below 38 degrees? 38 3.1 Density Curves Subscribe to view the full document.

Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 b. What proportion of the time is the January hi temperature below 38 degrees? Area= (base)(height) = (38-35)*(1/5) 38 3.1 Density Curves Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees. height = 35 40 b. What proportion of the time is the January hi temperature below 38 degrees? Area= (base)(height) = (38-35)*(1/5) 38 =3*.20 P(X<38)=.60 3.1 Density Curves Subscribe to view the full document.

Density Curves Example: Despite any rare arctic blasts, January high temperatures in Columbus tend to be uniformly distributed between 35 and 40 degrees.  ### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes