6. A manufacturing facility is producing components which are required to have a capacitance of 270 pF. In fact it has been found that the capacitance C is a ran- dom variable following a normal...

6. A manufacturing facility is producing components which are required to have a capacitance of 270 pF. In fact it has been found that the capacitance C is a ran- dom variable following a normal distribution with mean 271 pF and standard deviation 3.1 pF. Carry out the following calculations.

(a) Calculate the probability a component chosen at random will have a capac- itance less than 275 pF.

(b) Calculate the middle 95% of capacitances.