marks Window People Help x ADhttpswebooursesniuedu x vlpid38

marks Window People Help x ADhttps://weboourses.niu.edu x vlpid-3839396-dt-content-rid-23163122 2/courses/20152-ISYE-335-----1 Hw9%235 docx 8. A consumer electronics company is comparing the brightness of two different types of picture tubes for use in its television sets. Tube type A has mean brightness of 100 and standard deviation of 16, while tube type B has unknown mean brightness, but the standard deviation is assumed to be identical to that for type A. A random sample ofn- 25 tubes of each type is selected, and Xi X is computed. If puB equals or exceeds MA, the manufacturer would like to adopt type B for use. The observed difference is xB-RA 3.5. What decision would you make, and why? 10. The elasticity of a polymer is affected by the concen- tration of a reactant. When low concentration is used, the true mean elasticity is 55, and when high concentration is used the mean elasticity is 60.The,standard deviation ofelasticity is 4, regardless of concentration. If two random samples ofsize 16 are taken, find the probability that high Xlow z 2. Xt

Solution

(8) I adopt type B for use because the mean for B is larger than mean A

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(10)xbar_high - xbar_low follows mean=60-55=5 and

standard deviation =sqrt(4^2/16+2^2/16)=1.118034

So the probability is

P(xbar_high-xbar_low >=2)

=P((xbar_high-xbar_low)/s > (2-5)/1.118034)

=P(Z>-2.68) =0.9963 (from standard normal table)