A certain machine makes electrical resistors having a mean resistance

1.	A certain machine makes electrical resistors having a mean resistance of 40 ohms and a standard deviation of 2 ohms. Assuming that the resistance follows a normal distribution and can be measured to any degree of accuracy, what percentage of resistors will have a resistance that exceeds 43 ohms?
Answer» $\large\underline{\bf{Solution-}}$ Let X be the random variable which REPRESENTS the resistance of an electrical resistor. Given that, Mean resistance of electrical resistor = 40 ohms $\rm :\longmapsto\: \mu \: = 40 \: ohms$ Standard deviation of electrical resistor = 2 ohms $\rm :\longmapsto\: \sigma \: = \: 2 \: ohms$ Let Z be a NORMAL variable CORRESPONDING to X = 43, then $\rm :\longmapsto\:Z = \dfrac{X - \mu}{ \sigma}$ $\rm :\longmapsto\:Z = \dfrac{43 - 40}{2}$ $\rm :\longmapsto\:Z = \dfrac{3}{2}$ $\bf\implies \:Z = 1.5$ Now, we have to find, $\rm :\longmapsto\:P(X > 43)$ $\: \: \rm = \: \: P(Z > 1.5)$ $\: \: \rm = \: \: 0.5 - P(0 \leqslant Z \leqslant 1.5)$ $\: \: \rm = \: \: 0.5 - 0.4332$ $\: \: \rm = \: \: 0.0668$ Hence, $\red{ \boxed{ \rm \: The \: required \:\% \: age = 0.0668 × 100 = 6.68 \: \%}}$ Additional Information :- 1. In normal distribution, mean, median and mode are equal. 2. Normal distribution is SYMMETRIC around the mean. 3. Area under the normal curve is 1.