The mean mathematics SAT score for all people who took the SAT in a particular year was 514 with a standard deviation of 117. Assume the mathematics SAT score is normally distributed. a) Identify the individual, variable, type of variable in the context of this problem. The individual is a randomly selected a randomly selected person who take the SAT The variable information collected from each individual is mathematics SAT score This variable is a quantitative -- discrete variable. b) What is the wording of the random variable X in the context of this problem? The random variable X = the mathematics SAT score of a randomly selected person who take the SAT c) Why can the Empirical Rule be used to approximate probabilities on this problem? The Empirical Rule can only be used to approximate probabilities for problems where the random variable has a normal distribution. It is given in the problem that the random variable has a normal distribution. d) Use the Empirical Rule to approximate the percentage of people who take the SAT that will have a mathematics SAT score between 397 and 865. There is about 0.8394 x % of people who take the SAT that will have a mathematics SAT score between 397 and 865. e) Use the Empirical Rule to approximate the percentage of people who take the SAT that will have a mathematics SAT score of at least 865 ? There is about 0.0013 x % of people who take the SAT that will have a mathematics SAT score of a least 865. The mean mathematics SAT score for all people who took the SAT in a particular year was 514 with a standard deviation of 117. Assume the mathematics SAT score is normally distributed. a) Identify the individual, variable, type of variable in the context of this problem. The individual is a randomly selected a randomly selected person who take the SAT The variable information collected from each individual is mathematics SAT score This variable is a quantitative -- discrete variable. b) What is the wording of the random variable X in the context of this problem? The random variable X = the mathematics SAT score of a randomly selected person who take the SAT c) Why can the Empirical Rule be used to approximate probabilities on this problem? The Empirical Rule can only be used to approximate probabilities for problems where the random variable has a normal distribution. It is given in the problem that the random variable has a normal distribution. d) Use the Empirical Rule to approximate the percentage of people who take the SAT that will have a mathematics SAT score between 397 and 865. There is about 0.8394 x % of people who take the SAT that will have a mathematics SAT score between 397 and 865. e) Use the Empirical Rule to approximate the percentage of people who take the SAT that will have a mathematics SAT score of at least 865 ? There is about 0.0013 x % of people who take the SAT that will have a mathematics SAT score of a least 865.