Question

Consider the following sample of observations on coating thickness for low-viscosity paint. 0.87 0.88 0.88 1.03 1.09 1.16 1.29 1.31 1.37 1.49 1.59 1.62 1.65 1.71 1.76 1.83 Assume that the distribution of coating thickness is normal (a normal probability plot strongly supports this assumption). (a) Calculate a point estimate of the mean value of coating thickness. (Round your answer to four decimal places.) 1.3456 State which estimator you used. (b) Calculate a point estimate of the median of the coating thickness distribution. (Round your answer to four decimal places.) 1.3456 State which estimator you used and which estimator you might have used instead. (Select all that apply.) ロロロロロ s/ (c) Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the remaining 90%. (Hint: Express what you are trying to estimate in terms of u and o.] (Round your answer to four decimal places.)

Answer 1

. a point estimate I mean value of coating thickness 1.34 5695 sampie mean cx is estimator of Population mean AS for normal distribution, meona medan paint estimate o median/-3456 estimator = * Pao = P(X7k) = 0.10 ie. Let k be the 90th percentie - P(x- U k-1)=0.10 cet x- -> NIOD s. - P(x-134564> K-1-3456 )-010 Plz 7-13456) = 0.10 K-1.3456 = 7010 0.3213 PP K-1-3456 0.3213 K: 1.28(0-3213) + €1.3456 = 1.7568 point estimate = 1.7568 ..

estimator uled - 96th Percentile o sai d) PCX (1.2) = P(x - 11 <1:2-4) 와생 이 - Plze 1.2-1.3456 0.3213 - P(Z <-0.4582) - P(Z (-0.45) = 0.32636 estimator = estimated standard more 0.3213 76 -0.02008 = 0.080325