The mean inside diameter of a sample of 200 washers manufact

The mean inside diameter of a sample of 200 washers manufactured by a machine is 0.502in, and the standard deviation is 0.005 in. The application for the washer permits a tolerance in the diameter of 0.4% in to 0.508 in. If the diameter is outside this tolerance, the washers are deemed defective and are sold as scrap. Assuming a normal distribution of washer diameters, What percentage of washers are discarded? If 20 000 washers are manufactured each day, how many washers are discarded daily? Twenty-five washers have a combined mass of 1 lb_m. IF the scrap dealer pays $0.85/lb_m how much money is recovered per day from the sale of scrap washers? The compressive strength of concrete specimens follows a normal distribution with a mean value of 2.75 ksi and a standard deviation of 0.30 ksi. IF the applied stress is 2.5 ksi, what is the probability of failure? To evaluate the performance of a certain brand of alkaline battery, researchers at a consumer testing laborator measure the lifetime of 160 1.5-volt batteries. Battery lifetime for this study is

Solution

7 a) Mean = 0.502 in

        Std Deviation = 0.005 in;

       Lower limit = 0.496 in

       Upper Limit = 0.508 in

       Considering a normal Distribution

       P( X = 0.496) = 0.11507

       P( X = 0.508) = 0.88493

       Therefore probability of no defect = 0.88493 - 0.11507 = 0.76986

       Hence Discard % = 1 - no defect = 23.014 %

b) For 20000 washers made everyday

    Discarded = 0.23014 * 20000 = 4603 washers

c) Money received   = 4603 * 0.85 / 25 = 156.5 $

8) Mean = 2.75 ksi

     Std Dev = 0.3 ksi

     P( X = 2.5 ksi) = 20.2328 % failure rate