A certain machine makes electrical resistors having mean resistance of 40 ohms and standard deviations of 2 ohms. Assuming that the resistance follows a normal distribution. What percentage of resistors will have a resistance exceeding 43 ohms? What percentage of registers will have a resistance between 30 ohms to 45 ohms?

Question

A certain machine makes electrical resistors having mean resistance of 40 ohms and standard deviations of 2 ohms. Assuming that the resistance follows a normal distribution.  What percentage of resistors will have a resistance exceeding 43 ohms? What percentage of registers will have a resistance between 30 ohms to 45 ohms?

Suresh Chand · Accepted Answer

X = resistance of resistors such that X ~ (μ, σ2) Given, μ = 40 σ = 2 σ2 = 4 x ~ (40, 4) Let z = (frac{x - μ}{σ}) be the standard normal variate. Solution i): p(x > 43) = (p(z > frac{x - μ}{σ})) = (p(z > frac{43 - 40}{2}) = p(z > 1.5) = 0.5 - p(0 < z < 1.5) = 0.5 - 0.4332 = 0.0668 Solution ii): p(30 ≤ x ≤ 45) = (pleft ( frac{30-40}{2} leq z leq frac{45 - 40}{2} right )) = p(-5 ≤ z ≤ 2.5) = p(-5 ≤ z ≤ 0) + p(0 ≤ z ≤ 2.5) = p(0 ≤ z ≤ 5) + p(0 ≤ z ≤ 2.5) = 0.5 + 0.4938 = 0.9938

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