3. The calibration of a scale is to be checked be weighing a 10-kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed With or = 2kg. Let ,u denote the true average weight reading on the scale. (a) What hypotheses should be tested? (b) Suppose the scale is to recalibrated if either g 2 10.1032 or g S 9.8968. What is the probability that recalibration is carried out when it is actually unnecessary? (c) What is the probability that recalibration is judged unnecessary when in fact a = 10.1? When ,u = 9.8? (d) Let z = 07%. For What value c is the rejection region in part (b) equivalent to the two-tailed rejection region: either 2: Z c or z 5 c? (e) If the sample size were only 10 rather than 25, how should the procedure in part (d) be altered so that oz 2 0.05