8.43 A certain type of resistor is marketed with the specification that the variance of resistances produced is around 50 ohms. A sample of 15 of these resistors is to be tested for resistances produced.

a Find the approximate probability that the sample variance S2 will exceed 80.

b Find the approximate probability that the sample variance S2 will be less than 20.

c Find an interval in which at least 75% of such sample variances should lie.

d What assumptions are necessary for your answers above to be valid?