# Handout10 - STOR 435 Handout 10 Sections 5.4-5.5 Example 1...

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STOR 435 Handout 10 Sections 5.4-5.5 Example 1 (Basic properties of Normal distribution) . 1. Let X be the score of a randomly picked student who took the SAT in 2003. Data suggests that this random variable has a N (1026 , 209). One often computes the standardized score Z = X - 1026 209 What is the distribution of this random variable? 2. If X has a N ( μ,σ ) distribution what is the distribution of Z = X - μ σ Use this to calculate E ( X ) and var ( X ) Example 2 (Example 4d; Probabilities using normal table) . An expert witness in a paternity suit testiFes that the length ( in days) of human gestation is approximately normally distributed with parameters μ = 270 and σ 2 = 100. The defendant in the suit is able to prove that he was out of the country during a period that began 290 days before the birth of the child and ended 240 days before the birth. If the defendant was, in fact, the father of the child, what is the probability that the mother could have had the very long or very short

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## Handout10 - STOR 435 Handout 10 Sections 5.4-5.5 Example 1...

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