Question: Sigma bonds experience free rotation at room

> The following data are the measures of the diameters of 36 rivet heads in 1/100 of an inch. (a) Compute the sample mean and sample standard deviation. (b) Construct a relative frequency histogram of the data. (c) Comment on whether or not there is any

> The percentage of wins for the Chicago Bulls basketball team going into the playoffs for the 1996–97 season was 87.7. Round the 87.7 to 90 in order to use Table A.1. (a) What is the probability that the Bulls sweep (4-0) the initial best-of-7 playoff ser

> The lengths of power failures, in minutes, are recorded in the following table. (a) Find the sample mean and sample median of the power-failure times. (b) Find the sample standard deviation of the power failure times. 22 18 135 15 90 78 69 98 102 8

> The following data represent the length of life, in seconds, of 50 fruit flies subject to a new spray in a controlled laboratory experiment: (a) Construct a double-stem-and-leaf plot for the life span of the fruit flies using the stems 0, 0Â&midd

> The following data represent the length of life in years, measured to the nearest tenth, of 30 similar fuel pumps: (a) Construct a stem-and-leaf plot for the life in years of the fuel pumps, using the digit to the left of the decimal point as the stem

> The following scores represent the final examination grades for an elementary statistics course: (a) Construct a stem-and-leaf plot for the examination grades in which the stems are 1, 2, 3, . . . , 9. (b) Construct a relative frequency histogram, draw

> A study of the effects of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it takes to fall asleep. These data are obtained: (a) Find the sample mean for each group. (b) Find the sample standard deviation for e

> Show that the n pieces of information in E(ri – )2 i=1 n Σα 2(ri – x) = 0. i=1

> Five independent coin tosses result in HHHHH. It turns out that if the coin is fair the probability of this outcome is (1/2)5 = 0.03125. Does this produce strong evidence that the coin is not fair? Comment and use the concept of P-value discussed in Sec

> A tire manufacturer wants to determine the inner diameter of a certain grade of tire. Ideally, the diameter would be 570 mm. The data are as follows: 572, 572, 573, 568, 569, 575, 565, 570. (a) Find the sample mean and median. (b) Find the sample varianc

> A manufacturer of electronic components is interested in determining the lifetime of a certain type of battery. A sample, in hours of life, is as follows: 123, 116, 122, 110, 175, 126, 125, 111, 118, 117. (a) Find the sample mean and median. (b) What fea

> For Exercise 1.6 on page 13, compute the sample standard deviation in tensile strength for the samples separately for the two temperatures. Does it appear as if an increase in temperature influences the variability in tensile strength? Explain. Data fro

> A national study that examined attitudes about antidepressants revealed that approximately 70% of respondents believe “antidepressants do not really cure anything; they just cover up the real trouble.” According to this study, what is the probability tha

> Consider the data in Exercise 1.5 on page 13. Compute the sample variance and the sample standard deviation for both control and treatment groups. Data in Exercise 1.5: Twenty adult males between the ages of 30 and 40 participated in a study to evaluate

> For the data of Exercise 1.4 on page 13, compute both the mean and the variance in “flexibility” for both company A and company B. Does there appear to be a difference in flexibility between company A and company B? D

> There is a 50-50 chance that the queen carries the gene of hemophilia. If she is a carrier, then each prince has a 50-50 chance of having hemophilia independently. If the queen is not a carrier, the prince will not have the disease. Suppose the queen has

> During bad economic times, industrial workers are dismissed and are often replaced by machines. The history of 100 workers whose loss of employment is attributable to technological advances is reviewed. For each of these individuals, it is determined if

> A survey of those using a particular statistical software system indicated that 10% were dissatisfied. Half of those dissatisfied purchased the system from vendor A. It is also known that 20% of those surveyed purchased from vendor A. Given that the soft

> A firm is accustomed to training operators who do certain tasks on a production line. Those operators who attend the training course are known to be able to meet their production quotas 90% of the time. New operators who do not take the training course o

> An industrial plant is conducting a study to determine how quickly injured workers are back on the job following injury. Records show that 10% of all injured workers are admitted to the hospital for treatment and 15% are back on the job the next day. In

> In the field of quality control, the science of statistics is often used to determine if a process is “out of control.” Suppose the process is, indeed, out of control and 20% of items produced are defective. (a) If three items arrive off the process line

> A construction company employs two sales engineers. Engineer 1 does the work of estimating cost for 70% of jobs bid by the company. Engineer 2 does the work for 30% of jobs bid by the company. It is known that the error rate for engineer 1 is such that 0

> A rare disease exists with which only 1 in 500 is affected. A test for the disease exists, but of course it is not infallible. A correct positive result (patient actually has the disease) occurs 95% of the time, while a false positive result (patient doe

> A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles are from out of state?

> A producer of a certain type of electronic component ships to suppliers in lots of twenty. Suppose that 60% of all such lots contain no defective components, 30% contain one defective component, and 10% contain two defective components. A lot is picked,

> A certain form of cancer is known to be found in women over 60 with probability 0.07. A blood test exists for the detection of the disease, but the test is not infallible. In fact, it is known that 10% of the time the test gives a false negative (i.e., t

> Consider the situation in Exercise 2.116, and suppose that the manufacturer can try only two combinations in a day. (a) What is the probability that any given set of two runs is chosen? (b) What is the probability that the highest temperature is used in

> A manufacturer is studying the effects of cooking temperature, cooking time, and type of cooking oil for making potato chips. Three different temperatures, 4 different cooking times, and 3 different oils are to be used. (a) What is the total number of co

> A certain federal agency employs three consulting firms (A, B, and C) with probabilities 0.40, 0.35, and 0.25, respectively. From past experience it is known that the probability of cost overruns for the firms are 0.05, 0.03, and 0.15, respectively. Supp

> A shipment of 12 television sets contains 3 defective sets. In how many ways can a hotel purchase 5 of these sets and receive at least 2 of the defective sets?

> From a box containing 6 black balls and 4 green balls, 3 balls are drawn in succession, each ball being replaced in the box before the next draw is made. What is the probability that (a) all 3 are the same color? (b) each color is represented?

> From 4 red, 5 green, and 6 yellow apples, how many selections of 9 apples are possible if 3 of each color are to be selected?

> In a certain federal prison, it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25 years of age or older. What is the probability that a prisoner sele

> The probability that a patient recovers from a delicate heart operation is 0.8. What is the probability that (a) exactly 2 of the next 3 patients who have this operation survive? (b) all of the next 3 patients who have this operation survive?

> The probability that a patient recovers from a delicate heart operation is 0.9. What is the probability that exactly 5 of the next 7 patients having this operation survive?

> A large industrial firm uses three local motels to provide overnight accommodations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 30% at the Lakeview Motor Lodge.

> If the probability is 0.1 that a person will make a mistake on his or her state income tax return, find the probability that (a) four totally unrelated persons each make a mistake; (b) Mr. Jones and Ms. Clark both make mistakes, and Mr. Roberts and Ms. W

> How many bridge hands are possible containing 4 spades, 6 diamonds, 1 club, and 2 hearts?

> The probabilities that a service station will pump gas into 0, 1, 2, 3, 4, or 5 or more cars during a certain 30-minute period are 0.03, 0.18, 0.24, 0.28, 0.10, and 0.17, respectively. Find the probability that in this 30-minute period (a) more than 2 ca

> The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint. Assume that the measurements are a simple random sample. (a) What is the sample size for the above sample? (b) Calculate the sample mean for thes

> An allergist claims that 50% of the patients she tests are allergic to some type of weed. What is the probability that (a) exactly 3 of her next 4 patients are allergic to weeds? (b) none of her next 4 patients is allergic to weeds?

> A truth serum has the property that 90% of the guilty suspects are properly judged while, of course, 10% of the guilty suspects are improperly found innocent. On the other hand, innocent suspects are misjudged 1% of the time. If the suspect was selected

> Denote by A, B, and C the events that a grand prize is behind doors A, B, and C, respectively. Suppose you randomly picked a door, say A. The game host opened a door, say B, and showed there was no prize behind it. Now the host offers you the option of e

> The manufacturer of a tricycle for children has received complaints about defective brakes in the product. According to the design of the product and considerable preliminary testing, it had been determined that the probability of the kind of defect in t

> There are two vacancies in a certain university statistics department. Five individuals apply. Two have expertise in linear models, and one has expertise in applied probability. The search committee is instructed to choose the two applicants randomly. (a

> A nationwide survey of college seniors by the University of Michigan revealed that almost 70% disapprove of daily pot smoking, according to a report in Parade. If 12 seniors are selected at random and asked their opinion, find the probability that the nu

> A random variable X that assumes the values x1, x2, . . . , xk is called a discrete uniform random variable if its probability mass function is f(x) = 1 k for all of x1, x2, . . . , xk and 0 otherwise. Find the mean and variance of X.

> Using the data in Table 6.1, predict the sign and magnitude of ΔH° for each of the following reactions. In each case, identify whether the reaction is expected to be endothermic or exothermic: From in Table 6.1: Br (а) + Bra +

> Identify the systematic name as well as the common name for each of the following compounds:

> Draw a Lewis dot structure for each of the following atoms: a. Carbon b. Oxygen c. Fluorine d. Hydrogen e. Bromine f. Sulfur g. Chlorine h. Iodine

> Indolizomycin is a potent antibiotic agent produced by a microorganism, called SK2-52. Of particular interest is the fact that SK2-52 is a mutant microorganism that was created in a laboratory from two different strains, Streptomyces teryimanensis and St

> Consider the structure of formaldehyde: a. Identify the type of bonds that form the C=O double bond. b. Identify the atomic orbitals that form each C−H bond. c. What type of atomic orbitals do the lone pairs occupy?

> Identify the electron configuration for each of the following ions: a. A carbon atom with a negative charge b. A carbon atom with a positive charge c. A nitrogen atom with a positive charge d. An oxygen atom with a negative charge

> a. Consider the figure shown in Problem 7.90. Compound 3 is most easily purified via recrystallization in water. As such, the product would have to be thoroughly dried in order to utilize IR spectral analysis to verify the conversion of 1 to 3. Explain w

> Pladienolide B is a macrocyclic (large ring) natural product isolated from an engineered strain of the bacterium Streptomyces platensis. An enantioselective, 31-step synthesis of it was reported18 in 2012—an improvement over a previousl

> Draw a Lewis structure of a carbon atom that is missing one valence electron (and therefore bears a positive charge). Which second-row element does this carbon atom resemble in terms of the number of valence electrons?

> Using E-Z designators, identify the configuration of each C=C double bond in the following compound:

> Consider the following four energy diagrams: a. Which diagrams correspond with a two-step mechanism? b. Which diagrams correspond with a one-step mechanism? c. Compare energy diagrams A and C. Which has a relatively larger Ea? d. Compare

> Consider the following reaction: a. Use Table 6.1 to estimate ΔH for this reaction. b. ΔS of this reaction is positive. Explain. c. Determine the sign of ΔG. d. Is the sign of ΔG dependent on temperatur

> In each of the following cases compare the bonds identified in red, and determine which bond you would expect to have the largest bond dissociation energy

> The following reaction gives a product with the molecular formula C4H8O2. Draw the structure of the product.

> George Olah was awarded the 1994 Nobel Prize in Chemistry for his research involving carbocations. An interesting series of carbocation rearrangements studied by Olah is shown below. Each of these rearrangements is accomplished via the migration of a met

> Which value of ΔG corresponds with Keq = 1? a. +1 kJ/mol b. 0 kJ/mol c. −1 kJ/mol

> Several natural products have been isolated from the flowering plant Sarcostemma acidum, which has been used in folk medicine as a cough suppressant. During efforts to make these compounds in the laboratory, it was discovered that one of the natural prod

> For each of the following multistep reactions, read the curved arrows and identify the sequence of arrow–pushing patterns:

> Most fabrics do a good job at protecting skin from exposure to sunlight, but addition of UV-absorbing compounds to clothing can further reduce the amount of ultraviolet light that passes through the fabric. The following transformation takes place upon a

> For each of the following cases, read the curved arrows and identify which arrow-pushing pattern is utilized:

> Name one element that you would expect to exhibit bonding properties similar to boron. Explain.

> Assign a systematic (IUPAC) name for each of the following compounds:

> Draw an energy diagram of a reaction with the following characteristics: a. A one-step reaction with a negative ΔG b. A one-step reaction with a positive ΔG c. A two-step reaction with an overall negative ΔG, where the intermediate is higher in energy

> Consider the following SN2 reaction: a. Assign the configuration of the chiral center in the substrate. b. Assign the configuration of the chiral center in the product. c. Does this SN2 process proceed with inversion of configuration? Explain. Br C

> (R)-(−)-Carvone is responsible for the characteristic minty odor and flavor of spearmint oil, and it can also serve as a useful chiral starting material for organic synthesis. A carbon-carbon π bond is normally nucleophilic,

> Identify all of the electrophilic centers in each of the following compounds: HO. (a) (b) Arachidonic acid A precursor in the biosynthesis of many hormones 2-Heptanone Used to control the population of Varroa mites in honey bee colonies

> For each of the following cases use the information given to determine whether or not the equilibrium will favor products over reactants: a. A reaction with Keq = 1.2 b. A reaction with Keq = 0.2 c. A reaction with a positive ΔG d. An exothermic rea

> Compare the Lewis dot structure of nitrogen and phosphorus and explain why you might expect these two atoms to exhibit similar bonding properties.

> Identify all of the nucleophilic centers in each of the following compounds: OH (a) 'Li (b) NH2 (c) (d)

> Consider the relative energy diagrams for four different processes: a. Compare energy diagrams A and D. Assuming all other factors (such as concentrations and temperature) are identical for the two processes, identify which process will occur more rapid

> In each of the following cases, use the data given to determine whether the reaction favors reactants or products: a. A reaction for which ΔG = +1.52 kJ/mol b. A reaction for which Keq = 0.5 c. A reaction carried out at 298 K, for which ΔH = +33 kJ/mol

> At room temperature, molecules spend most of their time in lower energy conformations. In fact, there is a general tendency for any system to move toward lower energy. As another example, electrons form bonds because they “prefer” to achieve a lower ener

> For each of the following reactions predict the sign of ΔG. If a prediction is not possible because the sign of ΔG will be temperature dependent, describe how ΔG will be affected by raising the temperature. a. An endothermic reaction for which the syste

> For each of the following carbocations determine if it will rearrange, and if so, draw the carbocation rearrangement with a curved arrow: (b) (c) (d) (f) (h) (6)

> For each of the following reactions determine whether ΔS for the reaction (ΔSsys) will be positive, negative, or approximately zero: Br HBr (a) HCI (b) + H20 + HCI (c) он (d) (е)

> For each of the following processes predict the sign of ΔS for the reaction. In other words, will ΔSsys be positive (an increase in entropy) or negative (a decrease in entropy)? || - (a) (b) (c) Br 0-H (d) (e) (f) OH

> (−)-Cameroonanol has been isolated from the essential oil of Echinops giganteus (globe thistle) plants and it is associated with a strong woody fragrance. Its structure, including relative stereochemistry, was confirmed when it was made

> Draw the curved arrows that accomplish each of the following transformations: H O-H H. (а) H 0-H он H H 0-H HOH (Ь) (c)

> Bromotriphenylmethane (compound 1) can be converted to 2a or 2b or 2c upon treatment with the appropriate nucleophile. a. Draw a mechanism for the conversion of 1 to 2b. b. In all three cases, conversion of 1 to 2 is observed to be nearly instantaneous

> Upon treatment with a strong base (such as NaOH), 2-naphthol (compound 1) is converted to its conjugate base (anion 2), which is then further converted into compound 3 upon treatment with butyl iodide. a. Draw the structure of 2, including a mechanism f

> For each of the following compounds, identify any polar covalent bonds by drawing δ+ and δ− symbols in the appropriate locations: H :F: H H-C-0-c--ċ-ö-c-H H-C-CI: H-C-Mg-Br: (a) H HH H (Ь) H (c) H H 10: H H

> The following reaction sequence was part of a stereocontrolled synthesis of cyoctol, used in the treatment of male pattern baldness. The third step in this process employs an uncharged nucleophile, affording an ion pair as the product (anion and cation).

> When you look up thermodynamic values in a table, such as bond dissociation energies or heats of combustion, did you ever wonder where all the numbers come from? You can thank the physical organic chemists whose research involves studying chemical reacti

> Control of stereochemistry is always an important consideration when designing a synthesis. Several techniques exist to invert the stereochemistry of secondary alcohols, and a newly developed method was used in the example shown below. Provide reagents t

> When a new synthetic method is developed, it is applied to a series of compounds to explore its utility. 4-Fluorophenylacetonitrile was used as a substrate in a synthetic methodology research paper. Provide a synthesis for 4-fluorophenylacetonitrile usin

> Propose a mechanism of formation for each of the following products: EIOH Нeat Br OEt OEt

> Consider the reaction below. The rate of this reaction is markedly increased if a small amount of sodium iodide is added to the reaction mixture. The sodium iodide is not consumed by the reaction and is therefore considered to be a catalyst. Explain how

> Which of the following reactions is expected to exhibit a faster rate? Explain CH;CH,Br Nal/EIOH CH;CH2I + Br NaCI / EIOH CH;CH,Br CH;CH;CI + Br

> Consider the reaction below, which involves both a dehydrogenation (removal of two neighboring hydrogen atoms) and a Diels-Alder reaction (which we will learn about in Chapter 16). Utilizing a specially designed catalyst, the achiral starting materials a

> The following compound can react rapidly via an SN1 process. Explain why this primary substrate will undergo an SN1 reaction so rapidly. OTs

> When butyl bromide is treated with sodium iodide in ethanol, the concentration of iodide quickly decreases, but then slowly returns to its original concentration. Identify the major product of the reaction.

> When (1R,2R)-2-bromocyclohexanol is treated with a strong base, an epoxide (cyclic ether) is formed. Suggest a mechanism for formation of the epoxide: OH Strong base 'Br An epoxide

> If you are having trouble paying attention during a long lecture, your levels of acetylcholine (a neurotransmitter) may be to blame. Identify any formal charges in acetylcholine. HH H HHC H III. H-C-C-0-c-C-N-C-H H H H H HC HHH Acetylcholine