3. Machine A makes parts whose lengths are approximately normally distributed with a mean of 4.6 mm and a standard deviation of 0.1 mm. Machine B makes parts whose lengths are approximately normally distributed with a mean of 4.9 mm and a standard deviation of 0.1 mm. Suppose that you have a box of parts which you believe are from Machine A, but you are not sure. You decide to test the hypothesis Ho: The parts are from Machine A. H1: The parts are from Machine B. by randomly selecting one part from the box and measuring it. (a) Draw the distributions for the lengths of parts from Machine A and from Machine B. For both sketches label the horizontal axis from 4.2 to 5.2 with 0.1 increments. Be sure to include all important features. (b) Suppose that you sample a part length of 4.8 mm. I. In your sketch for part (a), shade the region under the bell curve that corresponds to the p- value and clearly label the region as such. Il. Compute the p-value for your test. (c) What is your decision at the 0.01 level of significance? 4. General Electric produces a "soft white" 100-watt light bulb for which it states that the average life is 750 hours. Assume that the standard deviation is 120 hours. (a) suppose that a consumer agency randomly selects 100 of these bulbs and finds a sample mean life of 735 hours. Conduct an appropriate hypothesis test to determine if the consumer agency should doubt the manufacturer's claim. Calculate the p-value and explain how this value should be interpreted