A machine uses ball bearings from Companies E, F, and G in the ratio of 4:6:8
3. A machine uses ball bearings from Companies E, F, and G in the ratio of 4:6:8. The lower and upper specification limits under which the ball bearings are suitable for the machine are 190mm and 216mm, respectively. Experience has indicated that the actual diameter of a randomly selected ball bearing from Company E is normally distributed, with a mean 198mm and a variance 36mm-. The actual diameter of a randomly selected ball bearing from Company F is normally distributed, with a mean 205mm and a variance 64mm . The actual diameter of a randomly selected ball bearing from Company G is normally distributed, with the mean 210mm and the variance 100mm". (a) There is 90% probability that the diameter of a randomly selected ball bearing from Company E is greater than d. Find d. The orders from Companies E, F, and G are combined and mixed thoroughly. (b) Find the probability that a ball bearing selected randomly from the combined order is suitable for the machine. (c) Given that a ball bearing selected randomly from the combined order is suitable for the machine, find the probability that it is from Company E. 4. A clinic offers weight reduction treatments. It is assumed that the weight loss observed after a two-month treatment follows a normal distribution. From a simple random sample of 16 patients, the following weight reduction values (in pounds) are observed: 13.68, 7.07, 11.09, 9.02, 6.95, 11.53, 12.44, 9.66, 15.57, 7.04, 5.16, 11.1, 13.59, 9.84, 13.51, 15.6. (a) Suppose first that the population standard deviation of the weight reduction values is known and that, based on this population standard deviation, the margin of error at a confidence level of 95% for the mean weight reduction value for samples of size 64 is 0.735. Find and interpret an estimate for the mean weight reduction value based on the above sample of size 16 with 95% confidence. (b) Suppose next that the population standard deviation of the weight reduction values is not known and that, based on the sample provided, the margin of error for the mean weight reduction value is 1.7000. Find the critical value and significance level associated with this margin of error. In addition, find the corresponding confidence interval estimate for the mean weight reduction value. State clearly the level of confidence. (c) Find and interpret an estimate for the variance of the weight reduction values with 95% confidence based on the sample provided. (d) Suppose that in another random sample of 256 patients who lost weights of 11 pounds or above, 54% are females. Find and interpret an estimate for the percentage of males among all patients who lost a weight of 11 pounds or above with 95% confidence
