Please help me solve the following questions.

n the manufacture of a chemical product, several different layers of ink are deposited onto the surface. The thickness of these layers is critical if specifications regarding the final color are to be met. The thicknesses of two different layers of ink are considered random variables jointly distributed by the bivariate normal.

It is known that the first layer has a mean of 0.1 millimeters and a standard deviation of 3.1 millimeters, and the second layer has a mean of 0.23 millimeters and a standard deviation of 1.7 millimeters. Also, the correlation among the layers is 0.8. Moreover, specifications call for a product to have a thickness of the first layer in the range of 0.099 to 0.200 millimeters and for the second layer in the range of 0.230 to 0.250 millimeters (mm). Define random variables in your notes.

What is the variance of the sum of the two layers' thicknesses?

What is the covariance between layers?

Two technicians measured the surface finish of a metal part, obtaining the data presented in the table below. Assume that the measurements are normally distributed. The to test statistic was calculated for these measurements resulting in a value of to = 0.11. Using ox = 0.05 and assuming equal variances, the following test hypothesis was tested for the mean surface finish measurements made by the two technicians: Ho: M1 - /2 = 0, H1: /1 - /2 = 0 Based on the above information, which of the following statement(s) are correct? Technician 1 Technician 2 1.45 1.54 1.37 1.41 1.21 1.56 1.54 1.37 1.48 1.20 1.29 1.31 1.34 1.27 1.35CAMR 103 a. Repeat problem 5 if a statistical interchangeability is used. 405 #-002 (Diam ) 500 1 092 (Diam.1 EDO + 000 2501 .001 (Diam.) 2.000#.003 .245 + .001 (Diam.) Reference surface Figure 20. Sketch of three components prior to assembly.Trace metals In drinking water affect the flavor and an unusually high concentration can pose a health hazard. Ten pairs of data were taken measuring zinc concentration in bottom water and surface water of a water source. Zinc Zinc Location concentration in concentration in bottom water surface water 1 430 415 266 .238 567 390 4 .531 .410 5 .707 605 6 .716 .609 7 651 632 .589 .523 469 411 10 .723 612 Do the data support that the zinc concentration is less on the surface than the bottom of the water source, at the a = 0.1 level of significance? Note: A normal probability plot of difference in zinc concentration between the bottom and surface of water indicates the population could be normal and a boxplot Indicated no outliers. a. Express the null and alternative hypotheses in symbolic form for this claim. Assume My = M - /2, where is the population mean zinc concentration in the bottom of water and un is the mean zinc concentration in the surface of water. b. What is the significance level? 0.1 C. What is the test statistic? Round to 3 decimal places. IMG 4 S