(c) Find the probability that a randomly selected rod is defective.(d) Given that a randomly selected rod is defective, find the probability that it was producedby machine T. In a factory, machines R, S and T are all producing metal rods of the same length. Machine Rproduces 35% of the rods, machine S produces 40% and the rest are produced by machine T.Of their production of rods, machines R, S and T produce 4%, 5% and 3% defective rodsrespectively.

Answered: In a factory, machines R, S and T are…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Animals and people that take in more energy than they expend will get fatter. Here are data on 12 rhesus monkeys: 6 lean monkeys (4% to 9% body fat) and 6 obese monkeys (13% to 14% body fat). The data report the energy expended in 24 hours (kilojoules per minute) and the lean body mass (kilograms, leaving out fat) for each monkey. Lean Obese Body Mass Energy Body Mass Energy 6 1.13 8.2 0.91 8 1 9 1.32 9.2 1.46 10.4 1.18 10.5 1.62 12.7 1.46 9.2 1.02 12.2 1.28 9 1.16 10.6 1.37 (a) What is the mean lean body mass of the lean monkeys? ANSWER x¯=x¯= kilograms. (b) What is the mean lean body mass of the obese monkeys? ANSWER x¯=x¯= kilograms.
A diet supplies 0.8 grams of calcium per day, in addition to the nutrients listed in the table to the right. The amounts of calcium per unit (100 g) supplied by the three ingredients in the diet are as follows: 1.25 g from nonfat milk, 0.18 g from soy flour, and 0.8 g from whey. Another ingredient in the diet mixture is isolated soy protein, which provides the following nutrients in each unit: 78 g of protein, 0 g of carbohydrate, 3.6 g of fat, and 0.15 g of calcium. Complete parts (a) and (b) below. 0.42 X₁ x2 X3 11 34 45 3 0.8 CIES X4 (Type an integer or decimal for each matrix element.) Amounts (g) Supplied per 100 Amounts (g) g of Ingredient Supplied by Diet in One Day a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy protein necessary to supply precise amounts of protein, carbohydrate, fat, and calcium in the diet. Nutrient Nonfat Soy Whey Milk flour 36 Protein Carbohydrate 52 0 Fat 50 14 33 75 7 1.2 34 45 3
A nutritionist is performing an experiment on student volunteers. She wants to feed one of the volunteers a daily diet that consists of a combination of three commercial diet foods: MiniCal, LiquiFast, SlimQuick. For the experiment, it is important that the volunteer consume a total of exactly 500 of potassium, 75g of protein, and 1150 IU of vitamin D every day. The amounts of these nutrients in one ounce of eacl diet food are given in the table. How many ounces of each food should the volunteer eat every day to satisfy the nutrient requirements exactly? MiniCal (1 ounce) LiquiFast (1 ounce) SlimQuick (1 ounce) Potassium (mg) 50 75 10 Protein (g) 10 3 vitamin D (IU) 90 100 50 Solve the system algebraically or use the rref in your graphing calculator to find the amount of ounces of each food needed to satisfy the nutrient requirements.
In a tank containing 200 liters of freshwater, 50 kg of salt is poured instead of 40kg. To correct this condition, 10 liters of brine are allowed to flow out per minute while 10 liters of fresh water per minute are pumped into the tank. If the mixture is kept uniform by stirring, find the time required for the tank to contain the desired amount of salt.
A freshly brewed shot of espresso has three distinct components: the heart, body, and crema. The separation of these three components typically lasts only 10 to 20 seconds. To use the espresso shot in making a latte, a cappuccino, or another drink, the shot must be poured into the beverage during the separation of the heart, body, and crema. If the shot is used after the separation occurs, the drink becomes excessively bitter and acidic, ruining the final drink. Thus, a longer separation time allows the drink-maker more time to pour the shot and ensure that the beverage will meet expectations. An employee at a coffee shop hypothesized that the harder the espresso grounds were tamped down into the portafilter before brewing, the longer the separation time would be. An experiment using 24 observations was conducted to test this relationship. The independent variable Tamp measures the distance, in inches, between the espresso grounds and the top of the portafilter (i.e., the harder the…
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 567 milliliters of the drug, how many milliliters of compound A are needed?
A tent manufacture produces regular and expedition tents at three branches. Per hour of operation, the Harrogate branch produces 20 regular tents and 10 expedition tents. The Skipton branch produces 0 regular tents and 20 expedition tents, and the York branc h produces 80 regular tents and 20 expedition tents. In order to meet the demand, the company needs to produce exactly 240 regular tents and 100 expedition tents each day. How many hours per day should each branch operate in order to produce the required amounts of tent? Solve using Gauss-Jordan elimination method.
A freshly brewed shot of espresso has three distinct components: the heart, body, and crema. The separation of these three components typically lasts only 10 to 20 seconds. To use the espresso shot in making a latte, a cappuccino, or another drink, the shot must be poured into the beverage during the separation of the heart, body, and crema. If the shot is used after the separation occurs, the drink becomes excessively bitter and acidic, ruining the final drink. Thus, a longer separation time allows the drink-maker more time to pour the shot and ensure that the beverage will meet expectations. An employee at a coffee shop hypothesized that the harder the espresso grounds were tamped down into the portafilter before brewing, the longer the separation time would be. An experiment using 24 observations was conducted to test this relationship. The independent variable Tamp measures the distance, in inches, between the espresso grounds and the top of the portafilter (i.e., the harder the…
A researcher is interested in the effects of diazepam on anxiety in rats. She takes a group of 15 female rats and injects them with 0.005 mg of diazepam for every 100 g the rats weigh, and takes a different group of female rats and injects them with saline. She then puts them all on an elevated-plus maze for 15 minutes and observes how long they spend (in seconds) in the enclosed arms versus the open arms. The less time they spend in the enclosed arms means they have less anxiety. She also weighs them before the injection to make sure she gets the dosage correct. a. Identify the population of interest b. Identify the Independent variable. c. Identify the Dependent variable. d. What scale of measurement was used for the independent variable? Explain why you think so. e. Was the independent variable discrete or continuous? Explain why you think so. f. What scale of measurement was used for the dependent variable? Explain why you think so. g. How could you change the dependent measurement…
Consider a person who invests in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 6.5% on AAA bonds, 7% on A bonds, and 9% on B bonds. The person invests twice as much in B bonds as in A bonds. Let x, y and z represent the amounts invested in AAA, A, and B bonds, respectively. x + y + z = 10,000(total investment) 0.065x + 0.07y + 0.09z = 760(annual return) 2y – z = 0 Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond. Total Investment Annual Return $10,000 760

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In a factory, machines R, S and T are all producing metal rods of the same length. Machine R produces 35% of the rods, machine S produces 40% and the rest are produced by machine T. Of their production of rods, machines R, S and T produce 4%, 5% and 3% defective rods respectively.