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introduction to probability statistics

Questions and Answers of Introduction To Probability Statistics

Comparative Line and Bar Charts Suppose that the 105 students whose status was tabulated in Example 1.14 were from the University of Windsor (UW), and that an- other 100 students from an introductory
3.20 Chirping Crickets Male crickets chirp by rubbing their front wings together, and their chirping is temperature dependent. Crickets chirp faster with increasing temperature and slower with
3.18 LCD TVs, again As technology improves, the choice of televisions becomes more complicated. Should you choose an LCD TV, an LED TV, or a plasma TV? Does the price of an LCD TV depend on the size
3.17 Japanese Automakers in 2005 In 2005, total global production of motor vehicles was about 64 million units. The U.S. was the single largest producer with a 21% share of global output. Japan was
3.16 Students with Disabilities A social skills training program, reported in Psychology in the Schools, was implemented for seven students with mild disabilities in a study to determine whether the
3.15 Real Estate Prices The data relating the square metres of living space and the selling price of 12 residential properties given in Example 3.5 are reproduced here. First, find the best-fitting
3.14 Grocery Costs These data relating the amount spent on groceries per week and the number of household members are from Example 3.3:a. Find the best-fitting line for these data.b. Plot the points
3.13 The value of a quantitative variable is measured once a year for a 10-year period:a. Draw a scatterplot to describe the variable as it changes over time.b. Describe the measurements using the
3.12 Consider this set of bivariate data:a. Draw a scatterplot to describe the data.b. Does there appear to be a relationship between .x and y? If so, how do you describe it?c. Calculate the
Find the best-fitting line relating y to x for the following data. Plot the line and the data points on the same graph. X y 2 3 4 5 6 7 3.0 5.0 5.5 6.0 8.0 9.5
The data in Table 3.5 are the size of the living area (in m), X, and the selling price, Y, of 12 residential properties. The MINITAB scatterplot in Figure 3.6 shows a linear pattern in the data. x
A distributor of table wines conducted a study of the relationship between price and demand using a type of wine that ordinarily sells for $10 per bottle. He sold this wine in ten different marketing
The number of household members, X, and the amount spent on groceries per week, Y, are measured for six households in a local area. Draw a scatterplot of these six data points. x 2 2 3 4 1 5 y ($)
3.9 Facebook Fanatics, again Not only is the Facebook social networking site growing rapidly in North America, but the composition of Facebook members depends on both age and gender. During a
3.8 Charitable Contributions Canadians contrived their tradition of generosity toward charities in 2003. Their donation of $6.4 billion was an 11.4% increase from 2002. Again in 2005, Canadians
3.7 How Big Is the Household? A local chamber of commerce surveyed 126 households in its city and recorded the type of residence and the number of family members in each of the households. The data
3.6 Consumer Price Index The price of EX0306 living in Canada is continually increasing, as demonstrated by the consumer price indexes (CPIs) for food and shelter. These CPIs are listed in the table
3.5 How Much Free Time? When you were growing up, did you feel that you did not have enough free time? Parents and children have differing opinions on this subject. A research group surveyed 198
3.4 M&Ms The colour distributions for two snack- size bags of M&M candies, one plain and one peanut, are displayed in the table. Choose an appropriate graphical method and compare the
3.3 Consumer Spending The table below shows the average amounts spent per week by men and women in each of four spending categories:a. What possible graphical methods could you use to compare the
3.2 Province by Province A group of items are categorized according to a certain attribute-X, Y, Z-and according to the province in which they are produced:a. Create a comparative (side-by-side) bar
3.1 Gender Differences Male and female respon- dents to a questionnaire about gender differences are categorized into three groups according to their answers on the first question:a. Create
Along with the salaries for the 400 professors in Example 3.1, the researcher recorded two qualitative variables for each professor: rank and faculty. Table 3.2 shows the number of professors in each
Are professors in the faculty of science paid more than professors in the faculty of arts? The data in Table 3.1 were collected from a sample of 400 professors whose rank, faculty, and salary were
For a binomial distribution with find the smallest number n such that 1 success is more probable than no successes in n trials.
Refer to the population of social science majors in Exercise 5.118 but change the sample size to n = 5. Using the binomal table,(a) List the probability distribution.(b) Plot the probability
At one large midwest university, about 40% of the college seniors have a social science major.Fourteen seniors will be selected at random.Let X denote the number that have a social science major.
A viral infection is spread by contact with an infected person. Let the probability that a healthy person gets the infection in one contact be(a) An infected person has contact with six healthy
If in three Bernoulli trials the probability that the first two trials are both failures is 4/49, what is the probability that the first two are successes and the third is a failure?
Give an example ( different from those appearing in Exercise 5.107 ) of repeated trials with two possible outcomes where:(a) The model of Bernoulli trials is reasonable.(b) The condition of
Is the model of Bernoulli trials plausible in each of the following situations? Identify any serious violations of the conditions.(a) A dentist records if each tooth in the lower jaw has a cavity or
Refer to part (c) of Exercise 5.104. Calculate the mean and standard deviation of X.5.106 Let the random variable Y denote the proportion of times a head occurs in three tosses of a coin, that is,
Runs. In a row of six plants two are infected with a leaf disease and four are healthy. If we restrict attention to the portion of the sample space for exactly two infected plants, the model of
The cumulative probabilities for a distribution.A probability distribution can also be described by a function that gives the accumulated probability at or below each value of X.Specifically,(a)
A roulette wheel has 38 slots, of which 18 are red, 18 black, and 2 green. A gambler will play three times, each time betting $5 on red. The gambler gets $10 if red occurs and loses the bet
The number of days, X, that it takes the post office to deliver a letter between City A and City B has the probability distributionFind:(a) The expected number of days.(b) The standard deviation of
In the finals of a tennis match, the winner will get $60,000 and the loser $15,000. Find the expected winnings of player B if (a) the two finalists are evenly matched and (b) player B has probability
Refer to Exercise 5.92.(a) List the x values that lie in the interval m s to m s and calculate(b) List the x values that lie in the interval m 2s to m 2s and calculate
The following distribution has been proposed for the number of times a student will eat a gourmet restaurant dinner next week.(a) Calculate the mean and variance.(b) Plot the probability histogram
Refer to the monthly intersection accident data in Exercise 2.4. Considering an even longer record leads to a distribution for X =number of accidents in a month.(a) Calculate E (X).(b) Calculate sd
A list of the world's 10 largest companies, in terms of value, contains 5 from the United States, 3 from China, and 1 each from Germany and The Netherlands. A potential investor randomly selects 3 of
Refer to Exercise 5.87, but now suppose that the contents of the two lists are pooled together into a single larger list. Then two persons are drawn at random and without replacement.Let W denote the
Refer to Exercise 8.87 but now suppose the sampling is done in two stages: First a list is selected at random and then, from that list, two persons are selected at random without replacement.Let Y
A large science department at the university made a list of its top 20 juniors and top 30 seniors.The first list contains 8 females and the second 10 females. One person is randomly selected from
Refer to Exercise 5.83. A syndicated newspaper story reported that inspectors found 22 of 24 hamburgers underweight at restaurant W and fined that restaurant. Draw new control limits on your chart,
Refer to Exercise 5.83.(a) What are the unusual values for the number of underweight hamburgers in the sample if they correspond to proportions outside of the control limits of the p chart?(b) Use
Several fast food restaurants advertise quarterpound hamburgers. This could be interpreted as meaning half the hamburgers made have an uncooked weight of at least a quarter-pound and half have a
Refer to the credit card application approval process on page 209.(a) Make a p chart using the centerline and control limits calculated for(b) Suppose the next five weeks bring 12, 10, 15, 11, and 16
Many computer packages produce binomial probabilities.We illustrate the MINITAB commands for obtaining the binomial probabilities with n 5 and p .33. The probabilities P[X x ] are obtained by
The following table (see Exercise 5.58) shows the percentages of residents in a large community when classified according to gender and presence of a particular allergy. For each part below, find the
According to a recent report of the American Medical Association, 9.0% of practicing physicians are in the specialty area of family practice.Assuming that the same rate prevails, find the mean and
(a) For the binomial distribution with and list the probability distribution (x, f (x )) in a table.(b) From this table, calculate the mean and standard deviation by using the methods of Section
Calculate the mean and standard deviation of the binomial distribution using the formulas in mean = np s d √ n p (1p)(a) Exercise 5.65 if n is changed to 20.(b) Exercise 5.70 when n = 20.(c)
About 30% of adults say that reading is a favorite leisure activity. Let success be the outcome that reading is a favorite leisure activity.Find the probability that(a) More than 5 trials are needed
According to the U.S. Census Bureau, in 2007 about 10% of persons between 25 and 30 years old live alone. For a random sample of size n, use the binomial table to find the probability of(a) 1 or
Using the binomial table, find the probability of:(a) Four successes in 13 trials when p = .3.(b) Eight failures in 13 trials when p = .7(c) Eight successes in 13 trials when p = .3.Explain why you
Rh-positive blood appears in 85% of the white population in the United States. If 8 people are sampled at random from that population, find the probability that:(a) At least 6 of them have
Suppose 15% of the trees in a forest have severe leaf damage from air pollution. If 5 trees are selected at random, find the probability that:(a) Three of the selected trees have severe leaf
According to a recent survey, outside of their own family members, 26% of adult Americans have no close friend to confide in. If this is the prevailing probability today, find the probability that in
An interior designer makes a presentation to potential clients and this results in sales of her services in 35% of the cases. Let X denote the number of sales in the next four presentations.Assuming
(a) Plot the probability histograms for the binomial distributions for and p equal to .2, .5, and .8.(b) Locate the means.(c) Find for each of the three cases.
In each case, find the probability of x successes in n Bernoulli trials with success probability p for each trial. (a) x = 2 (b) x 3 n ===== 3 p = .35 = n = 6 = P .25 (c) x = 2 n = 6 p = .75
Construct a tree diagram for three Bernoulli trials. Attach probabilities in terms of p and q to each outcome and then table the binomial distribution for n 3.
The accompanying table shows the percentages of residents in a large community when classified according to gender and presence of a particular allergy.Suppose that the selection of a person is
An animal either dies (D) or survives (S) in the course of a surgical experiment. The experiment is to be performed first with two animals. If both survive, no further trials are to be made. If
According to the U. S. Census Bureau, in 2007 about 10% of persons between 25 and 30 years old live alone. Let S be the event a person lives alone. If five persons in that age group are randomly
Consider Bernoulli trials with success probability(a) Find the probability that four trials result in all failures.(b) Given that the first four trials result in all failures, what is the conditional
A market researcher intends to study the consumer preference between regular and decaffeinated coffee. Examine the plausibility of the model of Bernoulli trials in the following situations.(a) One
Refer to Exercise 5.49. Now suppose for each plot a fair coin will be tossed. If a head shows up, the plot will be treated; otherwise, it will be a control.With this manner of treatment allocation,
From four agricultural plots, two will be selected at random for a pesticide treatment. The other two plots will serve as controls. For each plot, denote by S the event that it is treated with the
Refer to Exercise 5.47 and suppose instead that the mix consists of 2500 candies, of which 600 are brown, 1200 are yellow, and 700 are of other colors. Repeat parts (a–c) of Exercise 5.47 in this
A jar contains 25 candies of which 6 are brown, 12 are yellow, and 7 are of other colors.Consider 4 successive draws of 1 candy at random from the jar and suppose the appearance of a yellow candy is
In each case, examine whether or not repetitions of the stated experiment conform to the model of Bernoulli trials. Where the model is appropriate, determine the numerical value of p or indicate how
Is the model of Bernoulli trials plausible in each of the following situations? Discuss in what manner (if any) a serious violation of the assumptions can occur.(a) Seven friends go to a blockbuster
Definition: The median of a distribution is the value m0 of the random variable such that and In other words, the probability at or below m0 is at least .5, and the probability at or above m0 is at
A salesman of small-business computer systems will contact four customers during a week. Each contact can result in either a sale, with probability .3, or no sale, with probability .7.Assume that
Given here are the probability distributions of two random variables X and Y.(a) From the X distribution, determine the distribution of the random variable 8 2X and verify that it coincides with the
Suppose the probability distribution of a random variable X is given by the functionCalculate the mean and standard deviation of this distribution. 12 f(x) = 25 - x for x = 1, 2, 3, 4
Upon examination of the claims records of 280 policy holders over a period of five years, an insurance company makes an empirical determination of the probability distribution of X number of claims
Refer to Exercise 5.35, but suppose that the projects are scheduled consecutively with A in the first year and B in the second year. The company’s chance of winning project A is still.50. Instead
A construction company submits bids for two projects. Listed here are the profit and the probability of winning each project.Assume that the outcomes of the two bids are independent.(a) List the
Referring to Exercise 5.27, find the mean and standard deviation of the number of customers.
Given the following probability distribution concerning Web sites visited almost every day:(a) Construct the probability histogram.(b) Find E(X), , and s. x * 1 f(x) .1 .2 -234 234 .3 .4
Among cable TV customers, let X denote the number of television sets in a single-family residential dwelling. From an examination of the subscription records of 361 residences in a city, the
Use the approximate probability distribution in Example 6 to calculate (a) P[X3] (b) P(X = 2] (c) P[2 X 3]
In a study of the life length of a species of mice, 120 newborn mice are observed. The numbers staying alive past the first, second, third, and fourth years are 106, 72, 25, and 0, respectively.Let X
Two probability distributions are shown in the following tables. For each case, describe a specific setting of random selection ( like the one given in Exercise 5.22) that yields the given
Consider the following setting of a random selection: A box contains 100 cards, of which 25 are numbered 1, 35 are numbered 2, 30 are numbered 3, 10 are numbered 4. One card will be drawn from the
A surprise quiz contains three multiplechoice questions: Question 1 has four suggested answers, Question 2 has three, and Question 3 has two. A completely unprepared student decides to choose the
Suppose, for a loaded die, the probabilities of the faces 1 2 3 4 5 6 are in the ratios 3 :1:1:1:1: 3. Let X denote the number appearing on a single roll of the die.(a) Determine the probability
New video games are rated, by editors, at various Web sites (e.g., www.gamespot.com). You are equally interested in five games that received editors' ratings ofon a ten point scale. Suppose you
Faced with a tight deadline on two major projects, you decide to hire two of the five available persons to help complete the work. They have 1, 2, 4, 2 and 1 years experience, respectively.Since
Each week a grocery shopper buys either canned (C) or bottled (B) soft drinks. The type of soft drink purchased in 3 consecutive weeks is to be recorded.(a) List the sample space.(b) If a different
Two of the integers {1, 3, 5, 6, 7} are chosen at random without replacement. Let X denote the difference larger minus smaller number.(a) List all choices and the corresponding values of X.(b) List
The random variable X takes on only the values 2, 4, 6, each with equal probability.The standard deviation of X equals 53 33 (b) 63 (c) 803 (d) 83 (e) w
The probability function f of the variable X is defined byThe distribution function of X is then given by f(x)= 1/3, if x = 0, 1/6, if x = 1, 1/2, if x = 2.
The probability function f of the variable X is defined byThen, the value of c is (a) 9∕55 (b) 55∕36 (c) 36∕55 (d) 55∕9 (e) 16∕55 1/8, if x = 1, f(x)=cx/16, if x = 2,3, or 4, 1/64, if x = 5.
The random variable X takes only the values 10 and 20, each with equal probability.The upper bound we get for the probability P(12 ≤ X ≤ 18) from Chebyshev’s inequality is 25∕9.Then the value
Consider the probability function of a discrete random variable X defined byThe expected value of X is 19∕5. 2x-1 f(x)= == Rx {1,2,3,4,5}. 25
A random variable X has distribution functionThen X is a continuous random variable. 0, F(t)= t < 0, 0t

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