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Among college-age students (18-24 years old), 9.2% have hypertension. During a blood-donor program conducted during finals week, a blood-pressure reading is taken first, revealing that out of 200 donors, 29 have hypertension. All answers to three places after the decimal. A 95% confidence interval for the true proportion of college students with hypertension during finals week is ( , ). We can be 80% confident that the true proportion of college students with hypertension during finals week is with a margin of error of . Unless our sample (of 200 donors) is among the most unusual 10% of samples, the true proportion of college students with hypertension during finals week is between and . The probability, at 60% confidence, that a given college donor will have hypertension during finals week is , with a margin of error of . Assuming our sample of donors is among the most typical half of such samples, the true proportion of college students with hypertension during finals week is between and . We are 99% confident that the true proportion of college students with hypertension during finals week is , with a margin of error of . Assuming our sample of donors is among the most typical 99.9% of such samples, the true proportion of college students with hypertension during finals week is between and . Covering the worst-case scenario, how many donors must we examine in order to be 95% confident that we have the margin of error as small as 0.01? Using a prior estimate of 15% of college-age students having hypertension, how many donors must we examine in order to be 99% confident that we have the margin of error as small as 0.01?
The firm forecasts that it could sell a maximum of 4,000 A-100's this week and a maximum of 1,000 B-200's. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. What are optimal weekly profits?
Recurrence relations with complex characteristic roots
Draw a rectangular box that has P and Q as opposite vertices and has its faces parallel to the coordinate planes. Then find the coordinates of the other six vertices of the box and the length of the diagonal of the box
Three-person Problem of Points
The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
Find a solution of the differential equation that satisfies the initial condition y(1) = 3.
Erika's cell-phone bill for july was $82. she sent a check for $50 and then made $37 worth of calls in August. How much did she then owe on her cell-phone bill?
A 150kg horizontal beam is supported at each end. A 380-kg piano rests a quarter of the way from one end. What is the vertical force on each of the supports?
Find the equation of the rational function that passes through (0,2), has a Horizontal Asymptote at y=3, a hole at x=1 and only one Vertical Asymptote at x=-2.
A square's side is increased by 7 yards, which corresponds to an increase in the area by 217 square yards. How many yards is the side of the initial square?
Let A and B be sets. Show that A x B and B x A have equal cardinality by constructing an explicit bijection between the two sets. Then use the following proposition to prove that multiplication is commutative. (Let n, m be natural numbers. Then nx..
Suppose that X1 and X2 are Gaussian random variables with means µ1 and µ2 respectively. Assume that µ1 ≠ µ2. The variance for each of the two random variables is σ2. Find the value of x for which fx1(x) = fx2(x).
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