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| m344 | Dave’s Automatic Door, referred to in Exercise 37, installs automatic garage door openers.
Based on a sample, following are the times, in minutes, required to install 10 door openers: 28, 32, 24, 46, 44, 40, 54, 38, 32, and 42.
a. Compute the sample variance.
b. Determine the sample standard deviation. |
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| m345 | David Wise handles his own investment portfolio, and has done so for many years. Listed below is the holding time (recorded to the nearest whole year) between purchase and sale for his collection of 36 stocks.
a. How many classes would you propose?
b. What class interval would you suggest?
c. What quantity would you use for the lower limit of the initial class?
d. Using your responses to parts (a), (b), and (c), create a frequency distribution.
e. Identify the appearance of the frequencydistribution. |
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| m346 | Davis Outboard Motors Inc. recently developed an epoxy painting process for corrosion protection on exhaust components. Bill Davis, the owner, wishes to determine whether the lengths of life for the paint are equal for three different conditions: saltwater, freshwater without weeds, and freshwater with a heavy concentration of weeds. Accelerated-life tests were conducted in the laboratory, and the number of hours the paint lasted before peeling was recorded. Five boats were tested for each condition.
Use the Kruskal-Wallis test and the .01 level to determine whether the lasting quality of the paint is the same for the three waterconditions. |
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| m347 | Decide whether a discrete or continuous random variable is the best model for each of the following variables:
(a) The time until a projectile returns to earth.
(b) The number of times a transistor in a computer memory changes state in one operation.
(c) The volume of gasoline that is lost to evaporation during the filling of a gas tank.
(d) The outside diameter of a machined shaft.
(e) The number of cracks exceeding one-half inch in 10 miles of an interstate highway.
(f) The weight of an injection-molded plastic part.
(g) The number of molecules in a sample of gas.
(h) The concentration of output from a reactor.
(i) The current in an electronic circuit. |
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| m348 | Define F on R3 by F(x) = (0, 0, cx3)x and let M be a compact three-dimensional manifold-with-boundary with MC {x: x3 <0}. The vector field F may be thought of as the downward pressure of a fluid of density in {x: x2 < 0}. Since a fluid exerts equal pressures in all directions, we define the buoyant force on M, due to the fluid, as −∫∂M <F,n >dA. Prove the following theorem. |
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| m349 | Define f: R -> R by
f (x) = { e-x-2 x ≠ 0,. 0 x -0,}
a. Show that f is a C00 function, and f(i) (0) = 0for all . |
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| m350 | Define g, h: {x€R2} |x| ≤ 1} ->R by
g(x,y) = (x,y, √1-x2-y2),
h(x,y) = (x,y, - √1-x2-y2), |
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| m351 | Define IP: Rn x Rn ->R by IP (x, y) = <x, y>.
(a) Find D(IP) (a,b) and (IP)’ (a,b).
(b) If f,g: R -> Rn are differentiable, and h: R -> R is defined by h(t) = <f(t), g(t)>, show that hI
(a) = .
(c) If f: R -> Rn is differentiable and |f(t) = 1 for all t, show that = 0. |
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| m352 | Define when a function f: Rn -> R is independent of the first variable and find f1 (a, b) for such f. Which functions are independent of the first variable and also of the second variable? |
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| m353 | DeKorte Tele-Marketing Inc. is considering purchasing a machine that randomly selects and automatically dials telephone numbers. DeKorte Tele-Marketing makes most of its calls during the evening, so calls to business phones are wasted. The manufacturer of the ma-chine claims that its programming reduces the calling to business phones to 15% of all calls. To test this claim, the director of purchasing at DeKorte programmed the machine to select a sample of 150 phone numbers. What is the likelihood that more than 30 of the phone numbers selected are those of businesses, assuming the manufacturer’s claim is correct? |
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| m354 | Derive the expressions for the mean and variance of a geometric random variable with parameter p. (Formulas for infinite series are required.) |
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| m355 | Derive the formula for the mean and standard deviation of a discrete uniform random variable over the range of integers. |
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| m356 | Derive the mean and variance of a hypergeometric random variable (difficult exercise). |
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| m357 | Describe the differences between a histogram and a dot plot. When might a dot plot be better than a histogram? |
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| m358 | Determine a value index for 2013 using 1990 as the baseperiod. |
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| m359 | Determine a value index for 2013 using 2000 as the baseperiod. |
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| m360 | Determine a value index for 2013 using 2000 as the baseperiod. |
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| m361 | Determine a value index for 2013 using 2000 as the baseperiod. |
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| m362 | Determine the constant c so that the following function is a probability mass function: for f(x) = cx for x = 1, 2, 3, 4. |
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| m363 | Determine the cumulative distribution function for the random variable in Exercise 3-20. |
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