Consider a binomial experiment with n = 10 and p = .10. a. Compute f(0). b. Compute f(2). c. Compute P(x 2). d. Compute P(x 1). e. Compute E(x). f. Compute Var(x) and .
A steel company in Hamilton can purchase Alberta coal at C $85 per metric ton (1000 kg) or West Virginia coal at US$65 per ton (20001b)(1 kg = 2.205 lb). How much cheaper in C$ per metric ton is the...
Three forces are exerted on an object placed on a tilted floor in Figure P3.43. The forces are measured in newtons (N). Assuming that forces are vectors, a. What is the component of the net force...
The Conch Caf, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy...
A hotel has 90 rooms. The table summarises information about the number of rooms occupied each day for a period of 200 days. i. Draw a cumulative frequency graph on graph paper to illustrate this...
If the diameter X [cm] of certain bolts has the density f(x) = k(x - 0.9)(1.1 - x) for 0.9 < x < 1.1 and 0 for other x, what are k, , and 2 ? Sketch f(x).
Craig wants to purchase a boat that costs $1,420. He signs an installment agreement requiring a 20% down payment. He currently has $250 saved. Does he have enough for the down payment?
Evaluate (counterclockwise). Show the details.
Discuss the pros and cons of telephone interviews that take place during dinner time in the early evening?
Assess whether there is a relationship between BMD at the femoral neck and cigarette smoking using CI methodology?
A random variable is uniformly distributed between 100 and 150. a. Draw the density function. b. Find P(X > 110). c. Find P(120 < X < 135). d. Find P(X < 122).
Repeat the analyses in Problem 12.67 for the mean change in TBUT at 5 minutes post-instillation vs. baseline? Data from 12.67 Use mixed effects methods to compare the mean change in TBUT immediately...
What are the estimated incidence rates in the ASA and control groups? Cancer Suppose we wish to study the association between aspirin intake and the incidence of colon cancer. We find that 10% of...
Adults aged 1950 need 1000 milligrams of calcium per day. Define a population that may have been used and explain how the sample might have been selected.
It is expected that aerobic square dancing during the 30-minute recess at an elementary school will help fight childhood obesity. a. State the research question. b. Identify the control and...
A researcher claims that at least 10% of all football helmets have manufacturing flaws that could potentially cause injury to the wearer. A sample of 200 helmets revealed that 16 helmets contained...
According to the National Center for Health Statistics, a 10-year-old male whose height is 53.5 inches has a height that is at the 15th percentile. Explain what this means.
The Federal Bureau of Investigation classifies various larcenies. The data in the next column represent the type of larcenies based on a random sample of 15 larcenies. What is the mode type of...
Suppose that Y has a bin(n, ) distribution. For the model, logit() = , consider testing H 0 : = 0 (i.e., = 0.5). Let = y/n. a. From Section 3.1.6, the asymptotic variance of = logit() is [n(l )]...
The article referred to in Exercise 23 presents values for the dependent and independent variables for 10 additional construction jobs. These values are presented in Tables SE24A and SE24B (page...
For a continuous random variable X, the number m such that P(X m) = 1/2 is called the median of X. (a) Find the median of an Exp() distribution. (b) Give a simplified expression for the difference...
Let X and Y have joint density f(x, y) = 12x(1 x), for 0 < x < y < 1. (a) Find the marginal densities of X and Y. (b) Find the conditional density of Y given X = x. Describe the conditional...
Evaluate the expression for the given value(s) of the variable. x 2 + 10x, x = 3
The Riveras are negotiating with two banks for a mortgage to buy a house selling for $105,000. The terms at bank A are a 10% down payment, an interest rate of 4%, a 30-year conventional mortgage, and...
The method of Lagrange multipliers assumes that the extreme values exist, but that is not always the case. Show that the problem of finding the minimum value of f (x, y) = x 2 + y 2 subject to the...
An Italian restaurant offers a choice of pasta or pizza meals. It costs $3 to make a pasta dish, which it sells for $13. The corresponding figures for pizzas are $2 and $10, respectively. The maximum...
Find the probability that a student passed, given that the student repeated the exam. Use the table, which shows the numbers of students from American Bar Association approved law schools who took...
The file MobileSpeed contains the overall download and upload speeds in mbps for nine carriers in the United States. Source: Data extracted from Best Mobile Network 2016, bit.ly/1KGPrMm, accessed...
An experimental design for a paired t test has 20 pairs of identical twins. How many degrees of freedom are there in this t test?
Are you an impulse shopper? A survey of 500 grocery shoppers indicated that 29% of males and 40% of females make an impulse purchase every time they shop. Assume that the survey consisted of 250...
The manager of the commercial mortgage department of a large bank has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these...
Does LTE network performance vary between providers? The file LTE contains the download speed (in Mbps) on LTE connections of AT&T and Verizon providers in 31 U.S. large metro markets. Source: Data...
A 2018 Pew Research Center survey (Pew Research website) examined the use of social media platforms in the United States. The survey found that there is a .68 probability that a randomly selected...
Determine the mean, median, and standard deviation of the following frequency distribution: Class Frequency 20 to under 30 30 to under 40 12 21 40 to under 50 50 to under 60 18 60 to under 70 12
Calculate the property taxes on a property assessed at $125 000 if the rate per $1000 is 22.751.
Two children are randomly selected from a group of five boys and seven girls. Determine which is more likely to be selected: a. Two boys or two girls? b. The two youngest girls or the two oldest boys?
Tablet PC Comparison provides a wide variety of information about tablet computers. Their website enables consumers to easily compare different tablets using factors such as cost, type of operating...
List the first five terms of the sequence. a 1 = 2, a 2 = 1, a n+1 = a n a n1
What is the expected overall prevalence of Alzheimers disease in the community if the prevalence estimates in Table 3.5 for specific agegender groups hold? Suppose a study of Alzheimers disease is...
What is the sensitivity using this cut-point? Genetics, Obstetrics Precise quantification of smoking during pregnancy is difficult in retrospective studies. Routinely collected blood specimens from...
It is of clinical interest to know if the duration of hospitalization is affected by whether a patient has received antibiotics. Answer this question descriptively using either numeric or graphic...
Draw 100 random samples from a binomial distribution, each based on 10 trials with probability of success = .05 on each trial. Obtain a frequency distribution of the number of successes over the 100...
Another way to score the visual analog scale is as a categorical variable where 50% improvement is considered a success and <50% improvement, remaining the same, or worsening is considered a failure....
In a NiCd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multiple oxidation states and that is usually found in the following states: Nickel Charge...
Find a function whose square plus the square of its derivative is 1.
Are the samples of the first E. coli count independent or dependent of the samples of the second E. coli count? Explain. As mentioned earlier, sand is used in the filter. Different filters had...
During the one-week period of January 1118, 2012, Facebook conducted an experiment to research whether emotional states can be transferred to others via emotional contagion. Facebook users were...
Reconsider the previous exercise about sex and coff ee consumption. The sample data could be organized in a two-way table as follows: a. Fill in the table with counts (which you make up) in such a...
Employee retention is a major concern for many companies. A survey of Americans asked how long they have worked for their current employer (Bureau of Labor Statistics website, December 2015)....
Let X Beta(a, b). Find the distribution of Y = 1 X.
Find the variance of a beta distribution with parameters a and b.
In another company, every worker received a 5% raise. How does this affect the mean salary? The standard deviation of the salaries?
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...
In an effort to inform political leaders and economists discussing the deregulation of electric and gas utilities, data on eight numerical variables from utility companies have been grouped using...
Let 2 (T) = i (T i i0 ) 2 / i0 . Then 2 (p) = X 2 /n, where X 2 is the Pearson statistic (1.15) for testing H 0 : i = i0 , i = 1, ..., N, and n 2 () is the noncentrality for that test when is...
Let X 1 and X 2 be independent, each with unknown mean and known variance 2 = 1. a. Let 1 = X 1 + X 2 /2. Find the bias, variance, and mean squared error of 1 . b. Let 2 = X 1 + 2X 2 /3. Find...
The consumption of caffeine to benefit alertness is a common activity practiced by 90% of adults in North America. Often caffeine is used in order to replace the need for sleep. One recent study...
Find the magnitude of the vector A = ( 3.00,4.00, 5.00).
A survey of 350 customers was taken at Regal Cinemas in Austin, Texas, regarding the type of movies customers liked. The following information was determined. 196 liked dramas. 153 liked comedies. 88...
Color the map by using a maximum of four colors so that no two regions with a common border have the same color. 3 6. 7. (5 6,
The outer and inner wheels are spun. Assuming that the wheels are independent and the outcomes are equally likely, determine the probability of obtaining. Numbers greater than 5 on both wheels. 3 2 4...
Find the limit. lim V3x 2 x-2*
A firm has 132 female and 88 male employees. (a) What percentage of staff are female? (b) During the next year 8 additional female staff are employed. If the percentage of female staff is now 56%,...
A monopolistic producer of two goods, G 1 and G 2 , has a total cost function TC = 5Q 1 + 10Q 2 where Q 1 and Q 2 denote the quantities of G 1 and G 2 , respectively. If P 1 and P 2 denote the...
A designer clothing firm makes ladies scarves and blouses using a blend of wool and silk fibres. The quantity of fibre (in grams) required for a scarf and a blouse, and the profit (in $s) made from...
The financial services call center in Problem 3.66 also monitors call duration, which is the amount of time spent speaking to customers on the phone. The file CallDuration contains the following data...
Akbar Overgrowth, from Exercise 27, estimates that the probability of a good growing season is 0.70. On that basis, In Exercise 27 KickGrass Lawncare is a service that cares for lawns in a large,...
The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, with a mean of $70000 and a standard deviation of $20000. A loan application is...
A sociologist is studying the relationship between consumption expenditures of families in the United States (Consumption in $), family income (Income in $), and whether or not the family lives in an...
Select a newspaper or magazine article that involves a statistical study, and write a paper answering these questions. a. Is this study descriptive or inferential? Explain your answer. b. What are...
Refer to Data Set 9 in Appendix B and consider the gross amounts from two different categories of movies: Movies with R ratings and movies with ratings of PG or PG-13. Do the results appear to...
Large Counts condition To use a Normal distribution to approximate binomial probabilities, why do we require that both np and n(1 p) be at least 10?
In Problem an augmented matrix for a system of linear equations in x, y, and z is given. Find the solution of each system. 1 1 2 -1 3 1 7 0 -2 4
What is the cost of an item that sells for $87.49 if a. The rate of markup on cost is 30%? b. The rate of markup on selling price is 30%?
A linear cost function is C(x) = 5x + 250. (a) What are the slope and the C-intercept? (b) What is the marginal cost, and what does it mean? (c) What are the fixed costs? (d) How are your answers to...
A $25,000, 91-day Province of Newfoundland Treasury bill was originally purchased at a price that would yield the investor a 1.438% rate of return if the T-bill is held until maturity. Thirty-four...
A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population...
(a) Find the unit tangent and unit normal vectors T(t) and N(t). (b) Use Formula 9 to find the curvature. r(t) = (1, t, r*)
The heights, in centimetres, of 54 children are represented in the following diagram. The children are split into two equal-sized groups: a tall half and a short half. Calculate an estimate of the...
An entertainer has been asked to give a performance consisting of four items. They know three songs, five jokes, two juggling tricks and can play one tune on the mandolin. Find how many different...
In a particular country, 90% of both females and males drink tea. Of those who drink tea, 40% of the females and 60% of the males drink it with sugar. Find the probability that in a random selection...
For the following exercises, use logarithms to solve. 8 10 p+7 7 = 24
A high-rate savings account pays interest of 3.05%. Interest is calculated on the daily closing balance and paid at the close of business on the last day of the month. A depositor had a $7255 opening...
Regina deposits $3,500 in a savings account that pays 1.05% interest, compounded semi-annually. In ag, round to the nearest cent. a. How much interest does the account earn in the first 6 months? b....
In Figure 2.61, estimate the marginal revenue when the level of production is 600 units and interpret it. 20,000 10,000 $ GA 0 600 Figure 2.61 R(q) 9
Every nonempty K-variety in F n may be written uniquely as a finite union V 1 U V 2 U U V k of affine K-varieties in F n such that V j V i for i j and each V i is irreducible (Exercise 8). Data...
Provide a point estimate and a 95% CI for the prevalence of otorrhea in the ear drop group? Otolaryngology Many children have tympanostomy tubes surgically inserted in their ears to reduce hearing...
a. In a taste test of a new beer 100 people rated the new beer and the leading brand on the market. The possible ratings were Poor, Fair, Good, Very good, and Excellent. The responses for the new...
A random sample of 300 circuits generated 13 defectives. (a) Use the data to test H 0 : p = 0.05 versus H 1 : p 0.05. Use = 0.05. Find the P-value for the test. (b) Explain how the question in part...
The data show the heights in feet of 14 roller coasters. Find the mean, median, midrange, and mode for the data. 102 105 125 50 91 95 102 120 160 95 118 160 50 84
Find the mean, variance, and standard deviation for the number of heads when 10 coins are tossed.
Consider the following computer output for an experiment. The factor was tested over four levels. (a) How many replicates did the experimenter use? (b) Fill in the missing information in the ANOVA...
An article in the Journal of Coatings Technology (1988, Vol. 60, pp. 2732) described a 24 factorial design used for studying a silver automobile basecoat. The response variable is distinctness of...
A worker in the automobile industry works an average of 43.7 hours per week. If the distribution is approximately normal with a standard deviation of 1.6 hours, what is the probability that a...
Iranian researchers studied factors affecting patients likelihood of wearing orthodontic appliances, noting that orthodontics is perhaps the area of health care with the highest need for patient...
The National Center for Health Statistics reports in Vital Statistics of the United States that the median birth weight of U.S. babies was 7.4 lb in 2002. A random sample of this years births...
Let P 1 and P 2 be two probability functions on . Define a new function P such that P(A) = (P 1 (A)+P 2 (A))/2. Show the P is a probability function.
Suppose you throw five dice and all outcomes are equally likely. (a) What is the probability that all dice are the same? (b) What is the probability of getting at least one 4? (c) What is the...
Two resistors, with resistances R 1 and R 2 , are connected in series. R 1 is normally distributed with mean 100 and standard deviation 5 , and R 2 is normally distributed with mean 120 and...
Sketch a histogram for which a. The mean is greater than the median. b. The mean is less than the median. c. The mean is approximately equal to the median.