Let X representtheSATscoreofanenteringfreshmanatUniversityX.Therandomvariable X is known to have a N(1200, 90) distribution. Let Y represent the SAT score of an entering freshman at University Y. The random variable Y is known to have a N(1215, 110) distribution. A random sample of 100 freshmen is obtained from each university. Let ¯ X =the sample mean of the 100 scores from University X, and ¯ Y = the sample mean of the 100 scores from University Y. (a) What is the probability that ¯ X will be less than 1190?(b) What is the probability that ¯ Y will be less than 1190? (c) What is the distribution of the difference in sample means between University X and University Y: ¯ X − ¯ Y? (d) What is the probability that ¯ X will be greater than ¯ Y?

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.