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...

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.

(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.

Jun 07, 2022

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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...

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