Applied Statistics and Probability for Engineers 6th Edition solutions

Applied Statistics and Probability for Engineers 6
X and Y are independent, normal random variables with \(E(X)=0, V(X)=4, E(Y)=10\), and \(V(Y)=9\). Determine the following: (a) \(E(2 x+3 Y)\) (b) \(V(2 X+3 Y)\) (c) \(P(2 X+3 Y<30)\) (d) \(P(2 X+3 Y<40)\) Equation transcription: Text trans

Applied Statistics and Probability for Engineers 6
X and Y are independent, normal random variables with \(E(X)=2, V(X)=5, E(Y)=6\) and \(V(Y)=8\). Determine the following: (a) \(E(3 X+2 Y)\) (b) \(V(3 X+2 Y)\) (c) \(P(3 X+2 Y<18)\) (d) \(P(3 X+2 Y<28)\) Equation transcription: Text transc

Applied Statistics and Probability for Engineers 6
Suppose that the random variable X represents the length of a punched part in centimeters. Let Y be the length of the part in millimeters. If E(X)=5 and V(X)=0.25, what are the mean and variance of Y?

Applied Statistics and Probability for Engineers 6
Problem 65E A plastic casing for a magnetic disk is composed of two halves. The thickness of each half is normally distributed with a mean of 2 millimeters, and a standard deviation of 0.1 millimeter and the halves are independent. (a) Determine the mean and standard deviation of the total thicknes

Applied Statistics and Probability for Engineers 6
Problem 66E Making handcrafted pottery generally takes two major steps: wheel throwing and fi ring. The time of wheel throwing and the time of fi ring are normally distributed random variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively.

Applied Statistics and Probability for Engineers 6
Problem 67E In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. The thickness of these layers is critical if specifications regarding the final color and intensity of light are to be met. Let X and Y denote the thickness of two dif

Applied Statistics and Probability for Engineers 6
Problem 68E The width of a casing for a door is normally distributed with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23 7/8 inches and a standard deviation of 1/16 inch. Assume independence. (a) Determine the mean and standar

Applied Statistics and Probability for Engineers 6
Problem 69E An article in Knee Surgery Sports Traumatology, Arthroscopy [Effect of Provider Volume on Resource Utilization for Surgical Procedures (2005, Vol. 13, pp. 273279)] showed a mean time of 129 minutes and a standard deviation of 14 minutes for ACL reconstruction surgery for high-volume hos

Applied Statistics and Probability for Engineers 6
Problem 70E An automated filling machine fills soft-drink cans, and the standard deviation is 0.5 fluid ounce. Assume that the fill volumes of the cans are independent, normal random variables. (a) What is the standard deviation of the average fill volume of 100 cans? (b) If the mean fi ll volume i

Applied Statistics and Probability for Engineers 6
Problem 71E The photoresist thickness in semiconductor manufacturing has a mean of 10 micrometers and a standard deviation of 1 micrometer. Assume that the thickness is normally distributed and that the thicknesses of different wafers are independent. (a) Determine the probability that the average

Applied Statistics and Probability for Engineers 6
Problem 72E Assume that the weights of individuals are independent and normally distributed with a mean of 160 pounds and a standard deviation of 30 pounds. Suppose that 25 people squeeze into an elevator that is designed to hold 4300 pounds. (a) What is the probability that the load (total weight)

Applied Statistics and Probability for Engineers 6
Weights of parts are normally distributed with variance \(\sigma_{2}\). Measurement error is normally distributed with mean 0 and variance \(0.5 \sigma^{2}\), independent of the part weights, and adds to the part weight. Upper and lower specifications are centered at \(3 \sigma\) about the process me

Applied Statistics and Probability for Engineers 6
A U-shaped component is to be formed from the three parts A, B, and C. See Fig. 5-18. The length of A is normally distributed with a mean of 10 mm and a standard deviation of 0.1 mm. The thickness of parts B and C is normally distributed with a mean of 2 mm and a standard deviation of 0.05 mm. Assume

Applied Statistics and Probability for Engineers 6
Consider the perimeter of a part in Example 5-32. Let \(X_{1}\) and \(X_{2}\) denote the length and width of a part with standard deviations 0.1 and 0.2 centimeters, respectively. Suppose that the covariance between \(\(X_{1}\)\) and \(X_{2}\) is 0.02. Determine the variance of the perimeter \(Y=2 X_

Applied Statistics and Probability for Engineers 6
Problem 76E Three electron emitters produce electron beams with changing kinetic energies that are uniformly distributed in the ranges [3, 7], [2,5], and [4, 10]. Let Y denote the total kinetic energy produced by these electron emitters. (a) Suppose that the three beam energies are independent. Det

Applied Statistics and Probability for Engineers 6
In Exercise , the monthly demand for MMR vaccine was assumed to be approximately normally distributed with a mean and standard deviation of and million doses, respectively. Suppose that the demands for different months are independent, and let denote the demand for a year (in millions of does). De

Applied Statistics and Probability for Engineers 6
The rate of return of an asset is the change in price divided by the initial price (denoted as r). Suppose that $10,000 is used to purchase shares in three stocks with rates of returns \(X_{1}, X_{2}, X_{3}\). Initially, $2500, $3000, and $4500 are allocated to each one, respectively. After one year,