Mathematics

2.7 make connections, through investigationusing dynamic statistical software, betweenthe normal distribution and the binomial andhypergeometric distributions for increasingnumbers of trials of the discrete distributions(e.g., recognizing that the shape of the hypergeometricdistribution of the number of maleson a 4-person committee selected from agroup of people more closely resembles theshape of a normal distribution as the sizeof the group from which the committee wasdrawn increases)Sample problem: Explain how the total areaof a probability histogram for a binomialdistribution allows you to predict the areaunder a normal probability distributioncurve.2.8 recognize a z-score as the positive or negativenumber of standard deviations from the meanto a value of the continuous random variable,and solve probability problems involvingnormal distributions using a variety of toolsand strategies (e.g., calculating a z-score andreading a probability from a table; using technologyto determine a probability), includingproblems arising from real-world applicationsSample problem: The heights of 16-month-oldmaple seedlings are normally distributedwith a mean of 32 cm and a standard deviationof 10.2 cm. What is the probability thatthe height of a randomly selected seedlingwill be between 24.0 cm and 38.0 cm?Mathematics Functionsof Data ManagementMDM4UPROBABILITY DISTRIBUTIONS117