Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 4.3, Problem 11E
A microbiologist wants to estimate the concentration of a certain type of bacterium in a wastewater sample. She puts a 0.5 mL sample of the waste-water on a microscope slide and counts 39 bacteria. Estimate the concentration of bacteria, per mL, in this wastewater, and find the uncertainty in the estimate.
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A microbiologist wants to estimate the concentration of a certain type of bacterium in a waste-water sample. She puts a 0.5 mL sample of the wastewater on a microscope slide and counts 39 bacteria. Estimate the concentration of bacteria, per mL, in this wastewater, and find the uncertainty in the estimate.
The quality control engineer at Palmer Industries is interested in estimating the tensile strength of steel wire based on its outside diameter and the amount of molybdenum in the steel. As an experiment, she selected 25 pieces of wire, measured the outside diameters, and determined the molybdenum content. Then she measured the tensile strength of each piece. The results of the first four are recorded in the table.
Tensile Strength
Outside Diameter
Amount of Molybdenum
Place
(PSI ) Y
(mm) X1
(Units) X2
A
11
0.3
6
B
9
0.2
5
C
16
0.4
8
D
12
0.3
7
Using a statistical software package, the QC engineer determined the multiple regression equation to be Y’=-0.5+20X1+1X2.
a) Based on the equation, what is the estimated tensile strength of a steel wire having an outside diameter of .35 mm and 6.4 units of molybdenum?
b) Interpret the value of b1 in the equation.
Calcium is essential to tree growth because it promotes the formation of wood and maintains cell walls. In 1990, the concentration of calcium in precipitation in a certain area was 0.15 milligrams per liter (mg/L). A random sample of
10 precipitation dates in 2007 results in the following data table. Complete parts (a) through (c) below.
Click the icon to view the data table.
(a) State the hypotheses for determining if the mean concentration of calcium precipitation has changed since 1990.
Но
Ho:
0.15 mg/L
H1:
0.15 mg/L
i Data Table
(b) Construct a 95% confidence interval about the sample mean concentration of calcium precipitation.
The lower bound is
The upper bound is
(Round to four decimal places as needed.)
0.237
0.067
0.224
0.126
0.081
0.131
0.075
0.171
0.314
0.091
(c) Does the sample evidence suggest that calcium concentrations have changed since 1990?
Print
Done
A. Yes, because the confidence interval does not contain 0.15 mg/L.
B. Yes, because the confidence interval contains…
Chapter 4 Solutions
Statistics for Engineers and Scientists
Ch. 4.1 - After scoring a touchdown, a football team may...Ch. 4.1 - A certain brand of dinnerware set comes in three...Ch. 4.1 - When a certain glaze is applied to a ceramic...Ch. 4.1 - Let X and Y be Bernoulli random variables. Let Z =...Ch. 4.1 - A penny and a nickel are tossed. Both are fair...Ch. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.2 - Let X Bin(7, 0.3). Find a. P(X = 1) b. P(X = 2)...Ch. 4.2 - Let X Bin(9, 0.4). Find a. P(X 6) b. P(X 2) c....Ch. 4.2 - Prob. 3E
Ch. 4.2 - At a certain airport, 75% of the flights arrive on...Ch. 4.2 - Of all the registered automobiles in a certain...Ch. 4.2 - A fair die is rolled 8 times. a. What is the...Ch. 4.2 - Of all the weld failures in a certain assembly,...Ch. 4.2 - A general contracting firm experiences cost...Ch. 4.2 - Several million lottery tickets are sold, and 60%...Ch. 4.2 - A quality engineer takes a random sample of 100...Ch. 4.2 - In a random sample of 100 parts ordered from...Ch. 4.2 - Of the items manufactured by a certain process,...Ch. 4.2 - Of the bolts manufactured for a certain...Ch. 4.2 - Gears produced by a grinding process are...Ch. 4.2 - A commuter must pass through three traffic lights...Ch. 4.2 - A distributor receives a large shipment of...Ch. 4.2 - A k out of n system is one in which there is a...Ch. 4.2 - Refer to Exercise 17 for the definition of a k out...Ch. 4.2 - A certain large shipment comes with a guarantee...Ch. 4.2 - An insurance company offers a discount to...Ch. 4.2 - A message consists of a string of bits (0s and...Ch. 4.2 - Let X Bin(n, p), and let Y = n X. Show that Y ...Ch. 4.2 - Porcelain figurines are sold for 10 if flawless,...Ch. 4.2 - Prob. 24ECh. 4.2 - (Requires material from Section 3.3.) Refer to...Ch. 4.2 - If p is a success probability, the quantity p/(1 ...Ch. 4.3 - Let X Poisson(4). Find a. P(X = 1) b. P(X = 0) c....Ch. 4.3 - The number of flaws in a given area of aluminum...Ch. 4.3 - In a certain city, the number of potholes on a...Ch. 4.3 - Geologists estimate the time since the most recent...Ch. 4.3 - Prob. 5ECh. 4.3 - One out of every 5000 individuals in a population...Ch. 4.3 - The number of hits on a certain website follows a...Ch. 4.3 - The number of cars arriving at a given...Ch. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - A microbiologist wants to estimate the...Ch. 4.3 - Two-dimensional Poisson process. The number of...Ch. 4.3 - The number of defective components produced by a...Ch. 4.3 - The probability that a certain radioactive mass...Ch. 4.3 - The number of flaws in a certain type of lumber...Ch. 4.3 - Grandma is trying out a new recipe for raisin...Ch. 4.3 - Mom and Grandma are each baking chocolate chip...Ch. 4.3 - Prob. 18ECh. 4.3 - Someone claims that a certain suspension contains...Ch. 4.3 - A physicist wants to estimate the rate of...Ch. 4.3 - Prob. 21ECh. 4.4 - Twenty air-conditioning units have been brought in...Ch. 4.4 - There are 30 restaurants in a certain town. Assume...Ch. 4.4 - The probability that a computer running a certain...Ch. 4.4 - A traffic light at a certain intersection is green...Ch. 4.4 - Refer to Exercise 4. Let Y denote the number of...Ch. 4.4 - Refer to Exercise 4. What is the probability that...Ch. 4.4 - If X Geom(p), what is the most probable value of...Ch. 4.4 - A process that fills packages is stopped whenever...Ch. 4.4 - A system is tested for faults once per hour. If...Ch. 4.4 - Prob. 10ECh. 4.4 - In a lot of 10 microcircuits, 3 are defective....Ch. 4.4 - A lot of parts contains 500 items, 100 of which...Ch. 4.4 - Ten items are to be sampled from a lot of 60. If...Ch. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - A thermocouple placed in a certain medium produces...Ch. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.5 - Find the area under the normal curve a. To the...Ch. 4.5 - Find the area under the normal curve a. To the...Ch. 4.5 - Let Z N(0, 1). Find a constant c for which a. P(Z...Ch. 4.5 - If X N(2, 9), compute a. P(X 2) b. P(1 X 7) c....Ch. 4.5 - The lifetime of a battery in a certain application...Ch. 4.5 - The temperature recorded by a certain thermometer...Ch. 4.5 - Scores on a standardized test are approximately...Ch. 4.5 - Weights of female cats of a certain breed are...Ch. 4.5 - The lifetime of a lightbulb in a certain...Ch. 4.5 - In a certain university, math SAT scores for the...Ch. 4.5 - Penicillin is produced by the Penicillium fungus,...Ch. 4.5 - Specifications for an aircraft bolt require that...Ch. 4.5 - A cylindrical hole is drilled in a block, and a...Ch. 4.5 - Shafts manufactured for use in optical storage...Ch. 4.5 - The fill volume of cans filled by a certain...Ch. 4.5 - The amount of paint required to paint a surface...Ch. 4.5 - A fiber-spinning process currently produces a...Ch. 4.5 - The area covered by 1 L of a certain stain is...Ch. 4.5 - Prob. 19ECh. 4.5 - The quality-assurance program for a certain...Ch. 4.5 - Two resistors, with resistances R1 and R2, are...Ch. 4.5 - The molarity of a solute in solution is defined to...Ch. 4.5 - A binary message m, where m is equal either to 0...Ch. 4.5 - Refer to Exercise 23. Assume that if m = 0, the...Ch. 4.5 - A company receives a large shipment of bolts. The...Ch. 4.5 - Prob. 26ECh. 4.6 - The lifetime (in days) of a certain electronic...Ch. 4.6 - The article Assessment of Dermopharmacokinetic...Ch. 4.6 - The body mass index (BMI) of a person is defined...Ch. 4.6 - The article Stochastic Estimates of Exposure and...Ch. 4.6 - If a resistor with resistance R ohms carries a...Ch. 4.6 - Refer to Exercise 5. Suppose 10 circuits are...Ch. 4.6 - The article Withdrawal Strength of Threaded Nails...Ch. 4.6 - Choose the best answer, and explain. If X is a...Ch. 4.6 - Prob. 9ECh. 4.6 - A manufacturer claims that the tensile strength of...Ch. 4.6 - Let X1,...., Xn be independent lognormal random...Ch. 4.7 - Let T Exp(0.45). Find a. T b. T2 c. P(T 3) d....Ch. 4.7 - The time between requests to a web server is...Ch. 4.7 - A catalyst researcher states that the diameters,...Ch. 4.7 - The distance between flaws on a long cable is...Ch. 4.7 - Refer to Exercise 3. Suppose that the diameters of...Ch. 4.7 - Someone claims that the waiting time, in minutes,...Ch. 4.7 - A certain type of component can be purchased new...Ch. 4.7 - A radioactive mass emits particles according to a...Ch. 4.7 - The number of traffic accidents at a certain...Ch. 4.7 - The distance between consecutive flaws on a roll...Ch. 4.7 - A light fixture contains five lightbulbs. The...Ch. 4.8 - Prob. 1ECh. 4.8 - Resistors are labeled 100 . In fact, the actual...Ch. 4.8 - Let T (4,0.5). a.Find T. b.Find T. c.Find P(T ...Ch. 4.8 - Prob. 4ECh. 4.8 - Prob. 5ECh. 4.8 - The lifetime, in years, of a type of small...Ch. 4.8 - Let T Weibull (0.5, 3). a.Find T. b.Find T....Ch. 4.8 - Prob. 8ECh. 4.8 - Prob. 9ECh. 4.8 - The lifetime of a certain battery is modeled with...Ch. 4.8 - The lifetime of a cooling fan, in hours, that is...Ch. 4.8 - Someone suggests that the lifetime T (in days) of...Ch. 4.8 - A system consists of two components connected in...Ch. 4.8 - Prob. 14ECh. 4.8 - Prob. 15ECh. 4.8 - Prob. 16ECh. 4.8 - Prob. 17ECh. 4.9 - Choose the best answer to fill in the blank. If an...Ch. 4.9 - Choose the best answer to fill in the blank. The...Ch. 4.9 - Let X1 and X2 be independent, each with unknown...Ch. 4.9 - Let X1,, Xn be a simple random sample from a N(,2)...Ch. 4.9 - Let X Geom (p). Find the MLE of p.Ch. 4.9 - Let X1, Xn be a random sample from a population...Ch. 4.9 - Maximum likelihood estimates possess the property...Ch. 4.9 - Let X1,, Xn be a random sample from a N(, 1)...Ch. 4.9 - Let X1, Xn be a random sample from a N(0,2)...Ch. 4.9 - Let X1,, Xn be a random sample from a N(,2)...Ch. 4.10 - Prob. 1ECh. 4.10 - As part of a quality-control study aimed at...Ch. 4.10 - Below are the durations (in minutes) of 40...Ch. 4.10 - Prob. 4ECh. 4.10 - Construct a normal probability plot for the PM...Ch. 4.10 - Construct a normal probability plot for the logs...Ch. 4.10 - Can the plot in Exercise 6 be used to determine...Ch. 4.10 - In the article Assessment of...Ch. 4.11 - Bottles filled by a certain machine are supposed...Ch. 4.11 - A 500-page book contains 250 sheets of paper. The...Ch. 4.11 - A commuter encounters four traffic lights each day...Ch. 4.11 - Among all the income-tax forms filed in a certain...Ch. 4.11 - Bags checked for a certain airline flight have a...Ch. 4.11 - The amount of warpage in a type of wafer used in...Ch. 4.11 - The time spent by a customer at a checkout counter...Ch. 4.11 - Drums labeled 30 L are filled with a solution from...Ch. 4.11 - The temperature of a solution will be estimated by...Ch. 4.11 - Among the adults in a large city, 30% have a...Ch. 4.11 - In a process that manufactures bearings, 90% of...Ch. 4.11 - A machine produces 1000 steel O-rings per day....Ch. 4.11 - Radioactive mass A emits particles at a mean rate...Ch. 4.11 - The concentration of particles in a suspension is...Ch. 4.11 - The concentration of particles in a suspension is...Ch. 4.11 - A battery manufacturer claims that the lifetime of...Ch. 4.11 - A new process has been designed to make ceramic...Ch. 4.11 - The manufacture of a certain part requires two...Ch. 4.11 - Seventy percent of rivets from vendor A meet a...Ch. 4.11 - Radiocarbon dating: Carbon-14 is a radioactive...Ch. 4 - An airplane has 100 seats for passengers. Assume...Ch. 4 - The number of large cracks in a length of pavement...Ch. 4 - Pea plants contain two genes for seed color, each...Ch. 4 - A simple random sample X1,,Xn is drawn from a...Ch. 4 - The Environmental Protection Agency (EPA) has...Ch. 4 - In the article Occurrence and Distribution of...Ch. 4 - Medication used to treat a certain condition is...Ch. 4 - A certain type of plywood consists of five layers....Ch. 4 - Prob. 9SECh. 4 - Prob. 10SECh. 4 - In a certain process, the probability of producing...Ch. 4 - A process that polishes a mirrored surface leaves...Ch. 4 - Prob. 13SECh. 4 - Prob. 14SECh. 4 - Thicknesses of shims are normally distributed with...Ch. 4 - The lifetime of a microprocessor is exponentially...Ch. 4 - Prob. 17SECh. 4 - Prob. 18SECh. 4 - A cereal manufacturer claims that the gross weight...Ch. 4 - Prob. 20SECh. 4 - Prob. 21SECh. 4 - Prob. 22SECh. 4 - Prob. 23SECh. 4 - Prob. 24SECh. 4 - Let X Geom(p). Let s 0 be an integer. a.Show...Ch. 4 - Prob. 26SECh. 4 - Prob. 27SECh. 4 - Prob. 28SECh. 4 - Prob. 29SECh. 4 - Prob. 30SE
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