Questions and Answers of Statistics Engineers Scientists

A college math department consisting of 10 faculty members must choose a department head, an assistant department head, and a faculty senate representative. In how many ways can this be done?
The element titanium has five stable occurring isotopes, differing from each other in the number of neutrons an atom contains. If X is the number of neutrons in a randomly chosen titanium atom, the
Refer to Exercise 5. Two candidates are randomly selected.a. List the equally likely outcomes.b. What is the probability that both are qualified?c. What is the probability that exactly one is
Refer to Exercise 4. a. Find the conditional probability mass function pY |X (y | 1). b. Find the conditional probability mass function pX|Y (x | 2). c. Find the conditional expectation E(Y | X =
The article “Integrating Risk Assessment and Life Cycle Assessment: A Case Study of Insulation” (Y. Nishioka, J. Levy, et al., Risk Analysis, 2002: 1003–1017) estimates that 5.6% of a certain
The article “Improved Bioequivalence Assessment of Topical Dermatological Drug Products Using Dermatopharmacokinetics” (B. N’Dri-Stempfer, W. Navidi, et al., Pharmaceutical Research,
Refer to Exercise 1.a. Find the conditional probability mass function pY |X (y |0).b. Find the conditional probability mass function pX|Y (x |1).c. Find the conditional expectation E(Y | X = 0).d.
The article €œVehicle-Arrival Characteristics at Urban Uncontrolled Intersections€ (V. Rengaraju and V. Rao, Journal of Transportation Engineering, 1995: 317€“323)
Is the sample mean always the most frequently occurring value? If so, explain why. If not, give an example.
Is the sample mean always equal to one of the values in the sample? If so, explain why. If not, give an example.
Refer to Table 1.2 (in Section 1.2). Construct a stem and leaf plot with the ones digit as the stem (for values greater than or equal to 10 the stem will have two digits) and the tenths digit as the
Sketch a histogram for whicha. The mean is greater than the median.b. The mean is less than the median.c. The mean is approximately equal to the median.
Refer to Exercise 5. True or false:a. If the proportion of defectives in the sample is less than 12%, it is reasonable to conclude that the new process is better.b. If the proportion of
Is it possible for the standard deviation of a list of numbers to equal 0? If so, give an example. If not, explain why not.
The figure below is a histogram showing the distribution of serum cholesterol level for a sample of men. Use the histogram to answer the following questions:a. Is the percentage of men with
To determine whether a sample should be treated as a simple random sample, which is more important: a good knowledge of statistics, or a good knowledge of the process that produced the data?
In a certain company, every worker received a $50-per-week raise. How does this affect the mean salary? The standard deviation of the salaries?
The article €œThe Selection of Yeast Strains for the Production of Premium Quality South African Brandy Base Products€ (C. Steger and M. Lambrechts, Journal of Industrial
The histogram below presents the compressive strengths of a sample of concrete blocks hardened for 28 days. One rectangle from the histogram is missing. What is its height? 0.3 0.25 0.2 0.15 0.1 0.05
A medical researcher wants to determine whether exercising can lower blood pressure. At a health fair, he measures the blood pressure of 100 individuals, and interviews them about their exercise
In another company, every worker received a 5% raise. How does this affect the mean salary? The standard deviation of the salaries?
Concerning the data represented in the following boxplot, which one of the following statements is true?i. The mean is greater than the median.ii. The mean is less than the median.iii. The mean is
Refer to Table 1.4 (in Section 1.3).TABLE 1.4a. Using the class intervals in the table, construct a histogram in which the heights of the rectangles are equal to the frequencies.b. Using the class
A medical researcher wants to determine whether exercising can lower blood pressure. She recruits 100 people with high blood pressure to participate in the study. She assigns a random sample of 50 of
A sample of 100 adult women was taken, and each was asked how many children she had. The results were as follows:Children012345Number of Women2722301272a. Find the sample mean number of children.b.
Each of 16 students measured the circumference of a tennis ball by four different methods, which were:Method A: Estimate the circumference by eye.Method B: Measure the diameter with a ruler, and then
Which of the following statistics cannot be determined from a boxplot?i. The medianii. The meaniii. The first quartileiv. The third quartilev. The interquartile range
Refer to Exercise 12.a. If the measurements for one of the methods were converted to inches (1 inch=2.54 cm), how would this affect the mean? The median? The quartiles? The standard deviation?b. If
A sample of 100 resistors has an average resistance of 50 Ω and a standard deviation of 5 Ω. A second sample of 100 resistors has an average resistance of 100 Ω and a standard deviation of 5 Ω.
The cumulative frequency and the cumulative relative frequency for a given class interval are the sums of the frequencies and relative frequencies, respectively, over all classes up to and including
The Editor€™s Report in the November 2003 issue of Technometrics provides the following information regarding the length of time taken to review articles that were submitted for publication
Let A and B be events with P(A) = 0.8 and P(A ∩ B) = 0.2. For what value of P(B) will A and B be independent?
The probability that a bearing fails during the first month of use is 0.12. What is the probability that it does not fail during the first month?
DNA molecules consist of chemically linked sequences of the bases adenine, guanine, cytosine, and thymine, denoted A, G, C, and T. A sequence of three bases is called a codon. A base may appear more
A fair coin is tossed until a head appears. What is the probability that more than three tosses are necessary?
Let A and B be events with P(A) = 0.5 and P(A ∩ Bc) = 0.4. For what value of P(B) will A and B be independent?
Refer to Exercise 1.a. Find the marginal probability mass function pX (x).b. Find the marginal probability mass function pY (y).c. Find Î¼X.d. Find Î¼Y.e. Find
A die (six faces) has the number 1 painted on three of its faces, the number 2 painted on two of its faces, and the number 3 painted on one face. Assume that each face is equally likely to come up.a.
A metallurgist is designing an experiment to determine the effect of flux, base metal, and energy input on the hardness of a weld. She wants to study four different fluxes, two different base metals,
The bottom of a cylindrical container has an area of 10 cm2. The container is filled to a height whose mean is 5 cm, and whose standard deviation is 0.1 cm. Let V denote the volume of fluid in the
A box contains 15 resistors. Ten of them are labeled 50 Ω and the other five are labeled 100 Ω.a. What is the probability that the first resistor is 100 Ω?b. What is the probability that the
In a certain type of automobile engine, the cylinder head is fastened to the block by 10 bolts, each of which should be torqued to 60N· m. Assume that the torques of the bolts are independent.a. If
A laminated item is composed of five layers. The layers are a simple random sample from a population whose thickness has mean 1.2 mm and standard deviation 0.04 mm.a. Find the mean thickness of an
In horse racing, one can make a trifecta bet by specifying which horse will come in first, which will come in second, and which will come in third, in the correct order. One can make a box trifecta
Four candidates are to be interviewed for a job. Two of them, numbered 1 and 2, are qualified, and the other two, numbered 3 and 4, are not. The candidates are interviewed at random, and the first
Refer to Exercise 4. The total number of assemblies that fail to meet specifications is X + Y.a. Find Î¼X+Y.b. Find ÏƒX+Y.c. Find P(X + Y = 3).Refer to Exercise 4. y 0.15 0.12
Two batteries, with voltages V1 and V2, are connected in series. The total voltage V is given by V = V1+V2. Assume that V1 has mean 12 V and standard deviation 1 V, and that V2 has mean 6 V and
A group of 18 people have gotten together to play baseball. They will divide themselves into two teams of 9 players each, with one team wearing green uniforms and the other wearing yellow uniforms.
Let X represent the number of tires with low air pressure on a randomly chosen car.a. Which of the three functions below is a possible probability mass function of X? Explain.b. For the possible
Three times each day, a quality engineer samples a component from a recently manufactured batch and tests it. Each part is classified as conforming (suitable for its intended use), downgraded
In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y
Refer to Exercise 3. Resistors are randomly selected from the box, one by one, until a 100 Ω resistor is selected.a. What is the probability that the first two resistors are both 50 Ω?b. What is
Two production lines are used to pack sugar into 5 kg bags. Line 1 produces twice as many bags as does line 2. One percent of the bags from line 1 are defective in that they fail to meet a purity
The lifetime of a certain transistor in a certain application has mean 900 hours and standard deviation 30 hours. Find the mean and standard deviation of the length of time that four transistors will
Refer to Exercise 17 for the definition of a k out of n system. For a certain 4 out of 6 system, assume that on a rainy day each component has probability 0.7 of functioning, and that on a nonrainy
The length of time to perform an oil change at a certain shop is normally distributed with mean 29.5 minutes and standard deviation 3 minutes. What is the probability that a mechanic can complete 16
Radiocarbon dating: Carbon-14 is a radioactive isotope of carbon that decays by emitting a beta particle. In the earth€™s atmosphere, approximately one carbon atom in 1012 is carbon-14.
A physicist wants to estimate the rate of emissions of alpha particles from a certain source. He makes two counts. First, he measures the background rate by counting the number of particles in 100
An insurance company offers a discount to homeowners who install smoke detectors in their homes. A company representative claims that 80% or more of policyholders have smoke detectors. You draw a
If p is a success probability, the quantity p/(1 − p) is called the odds. Odds are commonly estimated in medical research. The article “A Study of Twelve Southern California Communities with
Five specimens of untreated wastewater produced at a gas field had an average benzene concentration of 6.83 mg/L with a standard deviation of 1.72 mg/L. Seven specimens of treated waste water had an
In a sample of 20 bolts, the average breaking torque was 89.7 J with a standard deviation of 8.2 J. Assume that the breaking torques are normally distributed.a. Find a 99% prediction interval for the
The article ??Effect of Refrigeration on the Potassium Bitartrate Stability and Composition of ItalianWines?? (A. Versari, D. Barbanti, et al., Italian Journal of Food Science, 2002:45??52) reports a
Construct a 95% confidence interval for the population variance σ2 if a sample of size 25 has standard deviation s = 15.
The specification for the pull strength of a wire that connects an integrated circuit to its frame is 10 g or more. In a sample of 85 units made with gold wire, 68 met the specification, and in a
Construct a 99% confidence interval for the population standard deviation σ if a sample of size 8 has standard deviation s = 7.5.
A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven others (the controls) receive the standard treatment. The recovery
Breathing rates, in breaths per minute, were measured for a group of 10 subjects at rest, and then during moderate exercise. The results were as follows:Find a 95% confidence interval for the
Scores on the math SAT are normally distributed. A sample of 20 SAT scores had standard deviation s = 87. Construct a 98% confidence interval for the population standard deviation σ.
A group of 50 computer science students were taught introductory computer programming class with an innovative teaching method that used a graphical interface and drag-and-drop methods of creating
Scores on an IQ test are normally distributed. A sample of 18 IQ scores had standard deviation s = 8. Construct a 95% confidence interval for the population variance σ2.
The article “Tibiofemoral Cartilage Thickness Distribution and its Correlation with Anthropometric Variables” (A. Connolly, D. FitzPatrick, et al., Journal of Engineering in Medicine,
A sample of 10 diesel trucks were run both hot and cold to estimate the difference in fuel economy. The results, in mpg, are presented in the following table. (From €œIn-use Emissions from
Following are weights, in pounds, of 12 two-month old baby girls. Assume that the population is normally distributed. a. Find the sample standard deviation s. b. Construct a 95% confidence interval
The article “Occurrence and Distribution of Ammonium in Iowa Groundwater” (K. Schilling, Water Environment Research, 2002:177–186) describes measurements of ammonium concentrations (in mg/L) at
Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 12 boxes. Assume that the population is normally distributed. a. Find the sample standard
In a study of contamination at landfills containing construction and demolition waste, 42 leachate specimens were tested for the presence of several contaminants. Of the 42 specimens, 26 contained
The article “Case Study Based Instruction of DOE and SPC” (J. Brady and T. Allen, The American Statistician, 2002:312–315) describes an effort by an engineering team to reduce the defect rate
Following are interest rates (annual percentage rates) for a 30-year fixed-rate mortgage from a sample of lenders in Colorado on May 3, 2013. Assume that the population is normally
Refer to Exercise 9. A device will be manufactured in which two of the components in Exercise 9 will be connected in series. The components function independently, and the device will function only
Eight independent measurements were taken of the dissolution rate of a certain chemical at a temperature of 0°C, and seven independent measurements were taken of the rate at a temperature of
Refer to Exercise 9. In a separate experiment, 18 cars were outfitted with tires with tread type A, and another 18 were outfitted with tires with tread type B. Each car was driven 1000 miles. The
The article “Evaluation of Criteria for Setting Speed Limits on Gravel Roads” (S. Dissanayake, Journal of Transportation Engineering, 2011:57–63) counted the numbers of vehicles of various
A sample of size 101 from a normal population has sample standard deviation s = 40. The lower and upper 0.025 points of the χ2100 distribution are χ2100, 0.975 = 74.222 and χ2100, 0.025 = 129.561.
Measurements of the sodium content in samples of two brands of chocolate bar yield the following results (in grams): Find a 98% confidence interval for the difference between the mean sodium
In a certain year, there were 80 days with measurable snowfall in Denver, and 63 days with measurable snowfall in Chicago. A meteorologist computes (80 + 1)/(365 + 2) = 0.22, (63 + 1)/(365 + 2) =
Refer to Exercise 10. Use the normal approximation to estimate the critical values χ2100, 0.025 and χ2100, 0.975 for a 95% confidence interval, and construct a 95% confidence interval for σ.A more
The article €œPermeability, Diffusion and Solubility of Gases€ (B. Flaconneche, et al., Oil and Gas Science and Technology, 2001:262€“278) reported on a study of the
The article “Influence of Penetration Rate on Penetrometer Resistance” (J. Oliveira, M. Almeida, et al., Journal of Geo technical and Geo environmental Engineering, 2011:695–703) presents
Refer to Exercise 10. Use the more accurate normal approximation to estimate the critical values χ2100, 0.025 and χ2100, 0.975 for a 95% confidence interval, and construct a 95% confidence interval
The article “Occurrence and Distribution of Ammonium in Iowa Groundwater” (K. Schilling, Water Environment Research, 2002:177–186) describes measurements of ammonium concentrations (in mg/L) at
Each day a quality engineer selects a random sample of 50 power supplies from the day’s production, measures their output voltages, and computes a 90% confidence interval for the mean output
Stainless steels can be susceptible to stress corrosion cracking under certain conditions. A materials engineer is interested in determining the proportion of steel alloy failures that are due to
In the article “Bactericidal Properties of Flat Surfaces and Nanoparticles Derivatized with Alkylated Polyethylenimines” (J. Lin, S. Qiu, et al., Biotechnology Progress, 2002:1082–1086),
The following MINITAB output presents a confidence interval for a population mean.a. How many degrees of freedom does the Student€™s t distribution have?b. Use the information in the
The article “A Music Key Detection Method Based on Pitch Class Distribution Theory” (J. Sun, H. Li, and L. Ma, International Journal of Knowledge-based and Intelligent Engineering Systems,
A stock market analyst notices that in a certain year, the price of IBM stock increased on 131 out of 252 trading days. Can these data be used to find a 95% confidence interval for the proportion of
Refer to Exercise 9.a. Find a 90% upper confidence bound for the mean weight. b. Someone says that the mean weight is less than 1.585 g. With what level of confidence can this statement be
The concentration of carbon monoxide (CO) in a gas sample is measured by a spectrophotometer and found to be 85 ppm. Through long experience with this instrument, it is believed that its measurements
Refer to Exercise 11.a. Find a 95% upper confidence bound for the mean sugar content.b. The claim is made that the mean sugar content is greater than 11.7 g.With what level of confidence can this

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