The probability density function of the weight of packages delivered by a post office is $f(x)=70 /\left(69 x^{2}\right) \quad 1<x<70 pounds.$ (a) What is the probability a package weighs less than 10 pounds? (b) Determine the mean and variance of package weight. (c) If the shipping cost is $3 per pound, what is the average shipping cost of a package?

A two-engine jet transport has a loaded weight of 90,000 lb and a forward thrust of 9800 lb per engine during takeoff. If the transport requires 4800 ft of level runway starting from rest to become airborne at a speed of 140 knots (1 knot = 1.151 mi/hr), determine the average resistance R to motion over the runway length due to drag (air resistance) and mechanical retardation by the landing gear.

Consider the patient satisfaction survey data. Using only first-order terms, build regression models using the following techniques: (a) All possible regressions. Find the Cp and S values. (b) Forward selection. (c) Backward elimination. (d) Comment on the models obtained. Which model would you prefer? Data from a patient satisfaction survey in a hospital are shown in the following table:

$$\begin{matrix} \text{Observation} & \text{Age} & \text{Severity} & \text{Surg-Med} & \text{Anxiety} & \text{Satisfaction}\\ \text{1} & \text{55} & \text{50} & \text{0} & \text{2.1} & \text{68}\\ \text{2} & \text{46} & \text{24} & \text{1} & \text{2.8} & \text{77}\\ \text{3} & \text{30} & \text{46} & \text{1} & \text{3.3} & \text{96}\\ \text{4} & \text{35} & \text{48} & \text{1} & \text{4.5} & \text{80}\\ \text{5} & \text{59} & \text{58} & \text{0} & \text{2.0} & \text{43}\\ \text{6} & \text{61} & \text{60} & \text{0} & \text{5.1} & \text{44}\\ \text{7} & \text{74} & \text{65} & \text{1} & \text{5.5} & \text{26}\\ \text{8} & \text{38} & \text{42} & \text{1} & \text{3.2} & \text{88}\\ \text{9} & \text{27} & \text{42} & \text{0} & \text{3.1} & \text{75}\\ \text{10} & \text{51} & \text{50} & \text{1} & \text{2.4} & \text{57}\\ \text{11} & \text{53} & \text{38} & \text{1} & \text{2.2} & \text{56}\\ \text{12} & \text{41} & \text{30} & \text{0} & \text{2.1} & \text{88}\\ \text{13} & \text{37} & \text{31} & \text{0} & \text{1.9} & \text{88}\\ \text{14} & \text{24} & \text{34} & \text{0} & \text{3.1} & \text{102}\\ \text{15} & \text{42} & \text{30} & \text{0} & \text{3.0} & \text{88}\\ \text{16} & \text{50} & \text{48} & \text{1} & \text{4.2} & \text{70}\\ \text{17} & \text{58} & \text{61} & \text{1} & \text{4.6} & \text{52}\\ \text{18} & \text{60} & \text{71} & \text{1} & \text{5.3} & \text{43}\\ \text{19} & \text{62} & \text{62} & \text{0} & \text{7.2} & \text{46}\\ \text{20} & \text{68} & \text{38} & \text{0} & \text{7.8} & \text{56}\\ \text{21} & \text{70} & \text{41} & \text{1} & \text{7.0} & \text{59}\\ \text{22} & \text{79} & \text{66} & \text{1} & \text{6.2} & \text{26}\\ \text{23} & \text{63} & \text{31} & \text{1} & \text{4.1} & \text{52}\\ \text{24} & \text{39} & \text{42} & \text{0} & \text{3.5} & \text{83}\\ \text{25} & \text{49} & \text{40} & \text{1} & \text{2.1} & \text{75}\\ \end{matrix}$$

The regressor variables are the patient's age, an illness severity index (larger values indicate greater severity), an indicator variable denoting whether the patient is a medical patient (0) or a surgical patient (1), and an anxiety index (larger values indicate greater anxiety)

Use technology to solve each equation. Express your answer rounded to three decimal places. $e^{x}=x^{2}$

Suppose that

$$f(x) = e-^x$$

0 < x. Determine the following: a. P(1 < X) b. P(1 < X < 2.5) c. P(X = 3) d. P(X < 4) e. P(3 ≤ X) f. x such that P(x < X) = 0.10 g. x such that P(X ≤ x) = 0.10

Suppose that

$$f(x) = e-(^x-^4)$$

for 4 < x. Determine the following: a. P(1 < X) b. P(2 ≤ X < 5) c. P(5 - X) d. P(8 < X < 12) e. x such that P(X < x) = 0.90

An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement) when recognizing a speckle pattern on a high-resolution CRT screen. The data are as follows: 36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 39.30, and 49.71. Calculate the sample average and sample standard deviation. Construct a dot diagram of the data.

Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim. A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is more than 6 hours.

The half-cylindrical shell of mass m, radius r, and length b revolves about one edge along the z-axis with a constant rate $\omega$. Determine the angular momentum H of the shell with respect to the x-y-z axes.

An electronics engineer is interested in the effect on tube conductivity of five different types of coating for cathode ray tubes in a telecommunications system display device. The following conductivity data are obtained. If $\alpha = 0.05,$ can you isolate any differences in mean conductivity due to the coating type?

$$\begin{matrix} \text{Coating Type} & \quad & \quad & \text{Conductivity}\\ \text{1} & \text{143} & \text{141} & \text{150} & \text{146}\\ \text{2} & \text{152} & \text{149} & \text{137} & \text{143}\\ \text{3} & \text{134} & \text{133} & \text{132} & \text{127}\\ \text{4} & \text{129} & \text{127} & \text{132} & \text{129}\\ \text{5} & \text{147} & \text{148} & \text{144} & \text{142}\\ \end{matrix}$$

Find k such that the function below is a probability density function over the given interval. Then write the probability density function.

f(x) = ke$^x$, [0, 3]

The thickness of a conductive coating in micrometers has a density function of $$ 600 x-^2 for 100 μm < x < 120 μm. a. Determine the mean and variance of the coating thickness. b. If the coating costs $0.50 per micrometer of thickness on each part, what is the average cost of the coating per part? $$

For a discrete probability distribution function, what is the mean or expected value?

(a) find the median of the random variable with the probability density function given, and (b) find the probability that the random variable is between the expected value (mean) and the median. $f(x)=2(1-x) ;[0,1]$