PPT-Chapter 6.2 Applications of the Normal Distribution

Summer spending A survey found that women spend on average 14621 on beauty products during the summer months Assume the standard deviation is 2944 Find the percentage of women who spend less than 16000 Assume the variable is normally distributed. 1. 4. Continuous Random Variables and Probability Distributions. 4-1 Continuous Random Variables. 4-2 Probability Distributions and Probability Density Functions. 4-3 Cumulative Distribution Functions. History. Abraham de . Moivre. (1733) – consultant to . gamblers. . Pronunciation. .. Pierre Simon . Laplace – mathematician, astronomer, philosopher, determinist.. Carl Friedrich . Gauss – mathematician and astronomer.. Objectives:. For variables with relatively normal distributions:. Students should know the approximate percent of observations in a set of data that will fall between the mean and ± 1 . sd. , 2 . sd. Distributions. Definition. Many sets of data fit what is called a Normal Distribution: EG.  . Examples when the Normal distribution arises. Looking at the national averages for NCEA.. When measuring heights, weights, arm spans, hand spans . State:. Express the problem in terms of the observed variable . x. .. Plan:. Draw a picture of the distribution and shade the area of interest under the curve.. Do:. Perform calculations.. Standardize. 68%-95%-99.7% Rule. Areas under Normal Curve. Areas under Normal Curve(cont). Example: Normal Distribution. The brain weights of adult Swedish males are . approximately. normally distributed with mean μ = 1,400 g and standard deviation . . and Exponential Distributions. 5. Introduction. Several specific distributions commonly occur in a variety of business situations:. N. ormal distribution—a continuous distribution . characterized . AP Statistics. Unit 5. The Central Limit Theorem for Sample Proportions. Rather than showing real repeated samples, . imagine. what would happen if we were to actually draw many samples.. Now imagine what would happen if we looked at the sample proportions for these samples. . . and Exponential Distributions. 5. Introduction. Several specific distributions commonly occur in a variety of business situations:. N. ormal distribution—a continuous distribution . characterized . Section 2.2. Normal Distributions. After this section, you should be able to…. DESCRIBE and APPLY the 68-95-99.7 Rule. DESCRIBE the standard Normal Distribution. PERFORM Normal distribution calculations. Section 5-3 – Normal Distributions: Finding Values. A. We have learned how to calculate the probability given an . x. -value or a . z. -score. . In this lesson, we will explore how to find an . Understand affects of shifting and rescaling. Find percentile. (&Use percentile to find z-score). Use the 68-95-99.7 Rule . (Empirical Rule). Create a Normal Probability Plot. AP Statistics Objectives Ch6. Copyright © Cengage Learning. All rights reserved. 5 Joint Probability Distributions and Random Samples Copyright © Cengage Learning. All rights reserved. 5.4 The Distribution of the Sample Mean Dehaish. Outlines. Normal distribution. Standard normal distribution . Find probability when known z score . Find z score from known areas . Conversion to Standard normal distribution.. Sampling distribution of sample mean .