Exam 1 with Solutions - Statistics for the Sciences | MATH 3339, Exams of Statistics

Download Exam 1 with Solutions - Statistics for the Sciences | MATH 3339 and more Exams Statistics in PDF only on Docsity! Page: 2 of 7 1. (10 pts.) Four fishes caught from a lake have the following weights (in ounces): 31 36 87) 28 Find, for this sample: (a) the median (b) the mea rledy ~ Etter ae 4 $2 OOF: 2. (8 pts.) We know that P(A) = .4, P(B) = .5, P(AU B) =.7. Are the events A and B independent? poe. PA) PCE ) oe = PCA) pip) - PAN B ) f a Vet Cae fins x (Ip) [Mey « alte AVR end /  . (16 pts.) The p.d.f. of the random variable X is oe (16 pts.) (a) Compnie P(X < 0.5). O (b) Compute the mean of X. (c) Compute the expected value of X*. d\) lecxco, §) = f(x) = 3a: for O<Se¢<1, an Sa AOS | ee ae x 0 b) ie Oe Page: 3 of 7 d zero otherwise.  Page: 6 of 7 7. (20 pts.) Cars arrive at a gas station according to a Poisson process with a rate of 6 cars/hour. | D & (a) What is the eau ae that at most. 12 cars arrive in two hours? An KASS (2) Gade PC S12)=, e417 Wee ee ae  Page: 7 of 7 8. (20 pts.) The diameters of ball-bearings produced by a machine have a normal distribution with mean 0.5 inches and standard deviation 0.001 inches. The balls are acceptable if their diameter is within 0.002in of 0.5in (that is, in the range 0.5-0.002, 0.5+-0.002] inches), ee (a) What fraction of the balls is acceptable, at the current, setting of the machine? (b) The standard deviation can be adjusted (by retooling the machine). How mmch should the standard deviation he so that 98% of the produced balls are acceptable? Zia ee ee a : pe Gy 80| / : goth —o.00L- Mee -\ G 49F— ¢ ——__—. _ / if a We? ae e 1 do} aie 102 |