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According to the South Coast Air Quality Management District, the level of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain May day in downtown Los Angeles is approximated by where A(t) is measured in pollutant standard index and t is measured in hours, with t = 0 corresponding to 7 a.m. Find A \'(t) . Solution A(t) = 0.01t^3 ( t-7)^4 + 70.70 Applying product rule for A\'t so, A\'t = 3*0.01 *t^2 (t-7)^4 + 4*0.01 t^3 (t-7)^3 or, A\'t = 0.03t^2 *(t-7)^4 + 0.04*t^3*(t-7)^3.

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- According to the South Dakota Department of Health, the mean number of hours of TV viewing per week is higher among adult women than men. A recent study showed women spent an average of 29 hours per week watching TV and men 24 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups, and that the standard deviation among the women is 4.9 hours and is 5.4 hours for the men. (a) What percent of the women watch TV less than 35 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) (b) What percent of the men watch TV more than 20 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) (c) How many hours of TV do the four percent of women who watch the most TV per week watch? Find the comparable value for the men. (Round your answers to 3 decimal places.)
- Women Men Solution 1. We compute the Z-score as (35-29)/4.9=1.22. Now looking into the table P(Z>1.22)=1-P(Z<=1.22)=0.1112. Therefore 11.12% 2. Similarly, Z-score as (20-24)/5.4 = - 0.74. Now P(Z>-0.74)=0.7734 and thus 77.34% 3. i)Let's say that they watch X hrs a week. Then Z'=(X-29)/4.9. And it is given that P(Z>Z')=0.04. Therefore we get the value of Z'=1.75. And then X=37.5754 ii)Similarly, for men, Z'=1.75 and X=33.45

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