Normal Distribution

Pages C H A P T E R 6 The Normal Distribution Objectives Outline After completing this chapter, you should be able to 1 2 3 Identify distributions as symmetric or skewed. 4 Find probabilities for a normally distributed variable by transforming it into a standard normal variable. Introduction 6–1 Normal Distributions Identify the properties of a normal distribution. Find the area under the standard normal distribution, given various z values. 5 Find

Final Exam Review Questions Solutions Guide You will probably want to PRINT THIS so you can carefully check your answers. Be sure to ask your instructor if you have questions about any of the solutions given below. 1. Explain the difference between a population and a sample. In which of these is it important to distinguish between the two in order to use the correct formula? mean; median; mode; range; quartiles; variance; standard deviation. Solution: A sample is a subset of a population. A population

23. This term refers to how data spreads out or disperses within a distribution. (Points : 1) |        Variability        Critical region        Range        Mode | 24. Relevant data that are expressed in numerical form are called: (Points : 1) |        Qualitative data        Quantitative data        Standard data        Multiplicative data | 25. It is not necessary to look at the frequency distribution if the mean, median, and mode are known. (Points : 1) |        True

The normal distribution is a continuous, unimodal and symmetric distribution. For a typical normal distribution, a mesokurtic (which means to have a moderate peak and tails for a graph), definition is one that has a mean of 0 and a standard deviation of 1. While this is the case, there might be other normal distributions with means that are not 0 and a standard deviation that is not 1, for these cases, we use their means and standard deviation. For example, if a normal distribution had a mean of

points) 3. Suppose that a random sample of size 64 is to be selected from a population having [pic] and standard deviation 5. (a) What are the mean and standard deviation of the [pic] sampling distribution? Can we say that the shape of the distribution is approximately normal? Why or why not? (10 points) (b) What is the probability that [pic] will be within 0.5 of the population mean? (5 points) (c) What is the probability that [pic] will differ from the population

skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. a) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes. b) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes. c) Distribution is approximately

Student Exploration: Sight vs. Sound Reactions Vocabulary: histogram, mean, normal distribution, range, standard deviation, stimulus Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Most professional baseball pitchers can throw a fastball over 145 km/h (90 mph). This gives the batter less than half a second to read the pitch, decide whether to swing, and then try to hit the ball. No wonder hitting a baseball is considered one of the hardest things to do in sports! 1. What

Math 221 Week 6 Lab Submitted by: Merima Ceric Part 1. Normal Distributions and Birth Weights in America 1) What percent of the babies born with each gestation period have a low birth weight (under 5.5 pounds)? a) Under 28 = 99.88% The NORMDIST formula was used to calculate: =NORMDIST(5.5,1.88,1.99,True) X= 5.5 Mean= 1.88 Standard Deviation=1.19 b) 32 to 35 weeks = 43.83% The NORMDIST formula

at Weston Materials, Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution. a. Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect? z(29) = (29-32)/2 = -3/2 z(34) = (34-32)/2 = 1 z(32) = 0 P(32 < x < 34) = P(0< z < 1) = 0.34 b. What percent of

II. STATEMENT OF THE PROBLEM As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth Medical Center in upstate New York investigated the relationship between geographic location, health status ( healthy or one or more comorbidities), and depression.  Random samples of 20 healthy individuals were selected from three geographic locations: Florida, New York, and North Carolina.  Then, each was given a standardized test to measure depression