Let X be a standard normal random variable so that X∼N(0,1). For this problem you may want to refer to the table provided on Canvas. Recall, that Φ(x) denotes the standard normal CDF. (a) Find Φ(1.45). (b) Find x, such that Φ(x) = 0.4. (c) Based on the fact that Φ(1.645) = 0.95 find an interval in which X will fall with 95% probability. (d) Find another interval (different from the one in (c)) into which X will fall with 95% probability. Hint you may want to consider the symmetric properties of the standard normal distribution. (e) Find an interval with lower bound -1.9 into which X will fall with 95% probability. (f) Find an interval with upper bound 2.1 into which X will fall with 95% probability. (g) Among all possible intervals into which X falls with 95% probability, find the shortest one.

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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.