An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.

Find and simplify an expression for the area of five rows of x squares with side lengths of x centimeters.

Given a = {(1, , 5)(6,4)}, b = {(2,0)(4, ,5)(0, 0)) and c = {(1, 1)(0, 2)(0, 3)(0, ,5)}, answer the following multiple choice question: from the list of sets a, b, and c, state the domain of set b. domain of set b: {0, 6,5} domain of set b: {2, 4,-4, 0} set b does not have a domain

Consider the linear model for a two-stage nested design with b nested in a as given below. yijk=\small \mu + \small \taui + \small \betaj(i) + \small \varepsilon(ij)k , for i=1,; j= ; k=1, assumption: \small \varepsilon(ij)k ~ iid n (0, \small \sigma2) ; \small \taui ~ iid n(0, \small \sigmat2 ); \tiny \sum_{j=1}^{b} \small \betaj(i) =0; \small \varepsilon(ij)k and \small \taui are independent. using only the given information, derive the least square estimator of \small \betaj(i) using the appropriate constraints (sum to zero constraints) and derive e(msb(a) ).