PROBABILITY AND STATISTICS

Students will:

•Know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces

•Know the definition of conditional probability and use it to solve for probabilities in finite sample spaces

•Demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses

•Be familiar with the standard distributions (normal, binomial, and exponential) and can use them to solve for events in problems in which the distribution belongs to those families

•Determine the mean and the standard deviation of a normally distributed random variable

•Know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations

•Compute the variance and the standard deviation of a distribution of data

•Organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots

ADVANCED PLACEMENT PROBABILITY AND STATISTICS

Students will:

•Solve probability problems with finite sample spaces by using the rules for addition, multiplication, and complementation for probability distributions and understand the simplifications that arise with independent events

•Know the definition of conditional probability and use it to solve for probabilities in finite sample spaces

•Demonstrate an understanding of the notion of discrete random variable and can interpret the probability of an outcome as the area of a region under the graph of the probability density function associated with the random variable

•Know the definition of the variance of a discrete random variable and can determine the variance for a particular discrete random variable

•Demonstrate an understanding of the standard distributions (normal., binomial, and exponential) and can use the distributions to solve for events in problems in which the distribution belongs to those families

•Determine the mean and the standard deviation of a normally distribution random variable

•Know the central limit theorem and can use it to obtain approximations for problems of finite sample spaces in which the probabilities are distributed binomially

•Know the definitions of the mean, median, and mode of distribution of data and can compute each of them in particular situations

•Compute the variance and the standard deviation of a distribution of data

•Find the line of best fit to a given distribution of data by using least squares regression

•Know what the correlation coefficient of two variables means and are familiar with the coefficient's properties

•Organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots

•Be familiar with the notions of a statistic of a distribution of values, of the sampling distribution of a statistic, and of the variability of a statistic

•Know basic facts concerning the relation between the mean and the standard deviation of a sampling distribution and the mean and the standard deviation of the population distribution

•Determine confidence intervals for a simple random sample from a normal distribution of data and determine the sample size required for a desired margin of error

•Determine the P-value for a statistic for a simple random sample from a normal distribution

•Be familiar with the chi-square distribution and chi-square test and understand their uses