A manufacturer of personal computers sets tests competing br

A manufacturer of personal computers sets tests competing brands and finds that the amount of energy they require are normally distributed with a mean of 285 kwh and a standard deviation of 9.1 kwh. If the lowest 25% and the highest 30% are not included in a second round of tests, what are the upper and lower limits for the energy amounts of the remaining sets?

Solution

lowest 25% :P(Z < z) = 0.25 ->

from the standard normal table: z = -0.675(X - 285)/9.1 = -0.675 -> X = 285 - 0.675*9.1 = 278.8575

-> lower limit highest 30% :P(Z < z) = 0.7 ->

from the standard normal table: z = 0.525(X - 285)/9.1 = 0.525 -> X = 285 + 0.525*9.1 = 289.7775 -> upper limit

Answer 3