Statistics I20755 marksNumerical: normal distribution probabilityContinuous distribution
A certain machine makes electrical resistors having a mean resistance of 40 ohms and standard deviation of 2 ohms. Assuming that the resistance follows a normal distribution.(i) What percentage of resistors will have a resistance exceeding 43 ohms?(ii) What percentage of resistors will have a resist
A certain machine makes electrical resistors having a mean resistance of 40 ohms and standard deviation of 2 ohms. Assuming that the resistance follows a normal distribution.(i) What percentage of resistors will have a resistance exceeding 43 ohms?(ii) What percentage of resistors will have a resistance between 30 ohms to 45 ohms? [5]
- Mean resistance: $\mu = 40$ ohms - Standard deviation: $\sigma = 2$ ohms - Distribution: Normal Standardization formula: $$Z = \frac{X - \mu}{\sigma}$$ --- Z-score for X = 43: $$Z = \frac{43 - 40}{2} = \frac{3}{2} = 1.5$$ Probability: $$P(X 43) = P(Z 1.5) = 0.5 - P(0 < Z < 1.5)$$ From standard ...