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**axnman** **Que. 1** Consider a Gaussian PDF with µ = 20, σ = 30, a = 50 and b =80. Determine i)Probability that P(x>b)

ii)P(x ≤ b) Mr F says: Find Pr(X < 80).

iii)P(x ≤ - b) Mr F says: Find Pr(X < - 80) = Pr (X > 80) = 1 - Pr(X < 80).

iv)P(a ≤ x ≤ b) Mr F says: Find Pr(50 < X < 80) = Pr(X < 80) - Pr(X < 50).

**Que. 2** In a certain manufacturing process only shafts whose diameters are less than 1.5 inches can be used. Given the shaft diameters are normally distributed with mean (µ) 1.490 inches and standard deviation (σ) 0.005 inches, determine the percentage of shafts that are usable.