Question: A box of tulip bulbs contains six

> Six mice - Alpha, Tau, Omega, Pi, Beta, and Phi- are to serve as subjects. List all possible ways to split them into two groups with the first having 4 mice and the second 2 mice.

> Two gel pens, G el-1 and Gel-2, are compared on the basis of the number of weeks before they stop writing. Out of 27 persons available, 13 are randomly chosen to receive Gel-1 and the other 14 receive Gel-2. These are the only pens they use for writing.

> Three male and three female students recorded the number of times they used a credit card in one week. (a) Calculate s2pooled. (b) Give an estimate of the common standard deviation for the number of uses. (c) Evaluate the t statistic for testing equalit

> Suppose that measurements of the size of butterfly wings (cm) for two related species yielded the data (a) Calculate s2pooled. (b) Give an estimate of the common standard deviation for the wing size for the two species. (c) Evaluate the t statistic for

> Calculate the mean and median for each of the following data sets. (a) 3 6 2 5 4 (b) 4 3 8 5 (c) -4 0 -3 -1 2 -1 0

> The generic output below summarizes the data, given in Data Bank, on the pretest percent body fat in male and female students. Find a 99% confidence interval for the difference of mean percent body fat.

> In the experiment, cat lovers were also scored on the Introversion/Extroversion scale. Using the summary statistics for both cases Dog lovers: n1 = 66, x = 6.12, s1 = 1.75 Cat lovers: n2 = 352, x = 4.81, s2 = 1.47 (a) Test the null hypothesis of equal me

> In a study of interspousal aggression and its possible effect on child behavior, the behavior problem checklist (BPC) scores were recorded for 47 children whose parents were classified as aggressive. The sample mean and standard deviation were 7.92 and 3

> Refer to the confidence interval obtained in Exercise 10.12(b). If you were to test the null hypothesis that the mean satisfaction scores are equal versus the two-sided alternatives, what would be the conclusion of your test with a = .057 Data from Exer

> Workers in three occupations were questioned about satisfaction with their jobs. Suppose the number of responses in each of the four categories are Assign l to very dissatisfied, 2 to a little dissatisfied, 3 to moderately satisfied, and 4 to very satisf

> Perform a test of hypothesis that is intended to show that the mean for magazine 1 is more than 2 words larger than the mean for magazine 2. (a) Formulate the null and alternative hypotheses. (b) State the test statistic and the rejection region with a =

> A linguist wants to compare the writing styles in two magazines and one measure is the number of words per sentence. On the basis of 50 randomly selected sentences from each source, she finds Determine a 98% confidence interval for the difference in mean

> Grades for first semester are compared to those for second semester. The five one-semester courses biology, chemistry, English , history, and psychology must be taken next year. (a) Make a list of all possible ways to split the courses into two groups w

> Referring to Exercise 7.8, use a die to generate samples of size 3. Investigate the sampling distribution of the number of times a value 1 occurs in a sample of size 3. (a) Roll the die and assign X = 1 if 1 dot shows and X = 0, otherwise. Repeat until

> Using a die, generate a sample and evaluate the statistic. Then repeat many times and obtain an estimate of the sampling distribution. In particular, investigate the sampling distribution of the median for a sample of size 3 from the population distribut

> Calculate the mean and median for each of the following data sets. (a) 2 10 3 6 4 (b) 3 2 7 4

> To determine the time a cashier spends on a customer in the express lane, the manager decides to record the time to check-out for the customer who is being served at 10 past the h our, 20 past the hour, and so on. Will measurements collected in this mann

> A bride-to-be asks a prospective wedding photographer to show a sample of her work. She provides ten pictures. Should the bride-to-be consider this a random sample of the quality of pictures she will get? Comment.

> A random sample of size 2 is selected, with replacement, from the set of numbers { 0, 2, 6 }. (a) List all possible samples and evaluate x and s2 for each . (b) Determine the sampling distribution of X. (c) Determine the sampling distribution of s2.

> From the set of numbers { 3, 5, 7 }, a random sample of size 2 is selected with replacement. (a) List all possible samples and evaluate x for each. (b) Determine the sampling distribution of X.

> Suppose 2 boards are needed for an application and the minimum stiffness of the two is of interest. (a) By row, take the SO minimums of the stiffness values for adj a cent pairs. Calculate their sample mean and standard deviation. Compare their sample m

> Suppose 2 boards are needed for an application and the average stiffness of the two is of interest. (a) By row, take the SO means of the stiffness values for adjacent pairs in Table 7. Calculate their sample mean and standard deviation. Compare their sam

> Data obtained from asking the wrong questions at the wrong time or in the wrong place can lead to misleading summary statistics. Explain why the following collection procedures are likely to produce useless data. (a) To evaluate the number of students w

> The number of complaints per day, X, received by a cable TV distributor has the probability distribution (a) Find the expected number of complaints per day. (b) Find the standard deviation of the number of complaints. (c) What is the probability distri

> Refer to Table 5 on page 223. (a) Calculate the sample median for each sample. (b) Construct a frequency table and make a histogram. (c) Compare the histogram for the median with that given in Figure 3 for the sample mean. Does your comparison suggest

> The weight of an almond is normally distributed with mean .05 ounce and standard deviation .01 5 ounce. Find the probability that a package of 100 almonds weighs between 4.8 and 5 .3 ounces. That is, find the probability that X is between .048 and .053 o

> Referring to Exercise 2.20, construct a five-stem display for the magnitude of earthquakes. Data from Exercise 2.20: In a recent year, 35 sites around the world experienced earthquakes of magnitude greater than 6.5.

> According to the growth chart that doctors use as a reference, the heights of two-year-old boys are normally distributed with mean 34.5 inches and standard deviation 1.3 inches. For a random sample of 6 two-year-old boys, find the probability that the sa

> The heights of male students at a university have a nearly normal distribution with mean 70 inches and standard deviation 2.8 inches. If 5 male students are randomly selected to make up an intramural basketball team, what is the probability that the heig

> The result of a recent survey suggests that one plausible population distribution, for X = number of persons with whom an adult discusses important matters, can be modeled as a population having mean µ = 2.0 and standard deviation a = 2.0. A random sampl

> The distribution of personal income of full-time retail clerks working in a large eastern city has µ = $51 ,000 and ( = $5000. (a) What is the approximate distribution for X based on a random sample of 100 persons? (b) Evaluate P ( X > 51 ,500].

> Suppose the weights of the contents of cans of mixed nuts have a normal distribution with mean 32.4 ounces and standard deviation .4 ounce. (a) If every can is labeled 32 ounces, what proportion of the cans have contents that weigh less than the labeled

> A population has distribution Let X 1 and X2 be independent and each have the same distribution as the population. (a) Det ermine the missing elements in the table for the sampling distribution of X = (X1 + X2)/2. (b) Find the expected value of XÂ&

> According to a normal distribution with mean 115 and standard deviation 22 hundredths of an inch describes the variation in female salmon growth in freshwater. For a sample of size 6, determine the (a) Mean of X¯. (b) Standard deviation of X¯. (c) Dis

> Identify the parameter, statistic, and population when they appear in each of the following statements. (a) During a recent year, forty-one different movies received the distinction of generating the most box office revenue for a weekend. (b) A survey

> As suggested in Example 8, Chapter 6, the population of hours of sleep can be modeled as a normal distribution with mean 7. 2 hours and standard deviation 1.3 hours. For a sample of size 9, determine the (a) Mean of X¯. (b) Standard deviation of X¯. (c

> Suppose the number of different computers used by a student last week has distribution Let X1 and X2 be independent and each have the same distribution as the population. (a) Determine the missing elements in the table for the sampling distribution of X

> If the double-stem display still has too few stems, we may wish to construct a stem-and-leaf display with a separate stem to hold leaves O and I, 2 and 3, 4 and 5, 6 and 7, and a stem to hold 8 and 9. The resulting stem-and-leaf display is called a five-

> Using the sampling distribution determined for X = ( X1 + X2 ) / 2, verify that E [X] = µ and

> Using the sampling distribution determined for X = ( X1 + X2 ) / 2, verify that E [X] = µ and

> Determine the standard deviation of X for a random sample of size (a) 9, (b) 36, and ( c) 144. ( d) How does quadrupling the sample size change the standard deviation of X?

> The data suggests that one plausible model, for X = the number of accidents in one month, is a population distribution having mean µ = 2.6 and variance (2 = 2.4. Determine the standard deviation of X for a random sample of size (a) 25, (b) 100, and ( c)

> Refer to the data on earthquakes of magnitude greater than 6.5. The data suggests that one plausible model, for X = magnitude, is a population distribution having mean µ = 7 .OS and standard deviation u = .43. Calculate the expected value and standard de

> Refer to the velocity data for females. One plausible model for the population distribution has mean µ = 31.2 and standard deviation c, = 8.62 feet per second. Calculate the mean and standard deviation of X for a random sample of size (a) 4 and (b) 25.

> The population density function and that for the sampling distribution of X, for n = 2, are shown in Figure 6. Identify which one is the sampling distribution and explain your answer.

> Th e population density function and that for the sampling 2 distribution of X are shown in Figure 5. Identify which one is the sampling distribution and explain your answer.

> Identify each of the following as either a parameter or a statistic. (a) Population standard deviation. (b) Sample interquartile range. (c) Population 20th percentile. (d) Sample first quartile. (e) Sample median.

> A file cabinet has 8 student folders arranged alphabetically according to last name. Three files are selected at random. (a) How many different selections are possible? (b) Find the probability that the selected folders are all adjacent.

> If there are too many leaves on some stems in a stem-and-leaf display, we might double the number of stems. The leaves 0- 4 could hang on one stem and 5- 9 on the repeated stem. For the observations. We would get the double-stem display Construct a doubl

> Refer to Exercise 4.91, and further suppose that the 5 respondents who are below 30 consist of 2 males and 3 females, whereas those above 30 consist of 4 males and 2 females. Now, the researcher wants to randomly select 2 males and 2 females to be assign

> An advertisement seeking volunteers for a clinical research draws 11 respondents. Of these respondents, 5 are below age 30 and 6 are over 30. The researcher will randomly select 4 persons to assign to a particular treatment regimen. (a) How many selecti

> Are the following methods of selection likely to produce a random sample of 5 students from your school? Explain. (a) Pick 5 students throwing flying discs on the mall. (b) Pick 5 students who are studying in the library on Friday night. (c) Select 5

> There are four elementary outcomes in a sample space. If P(e1) = .3, P(e2) = .4, and P(e3) = .2, what is the probability of e4?

> In one area city park, there are 15 trees, of which 9 are bushy and 6 that are not bushy. If 5 trees are selected at random to receive a new spray, what is the probability that exactly 3 bushy trees are selected?

> Nine agricultural plots for an experiment are laid out in a square grid as shown. Three plots are to be selected at random . (a) Find the probability that all 3 are in the same row. (b) Find the probability that all 3 are in different rows.

> A college senior is selected at random from each state. Next, one senior is selected at random from the group of 50. Does this procedure produce a senior selected at random from those in the United States?

> Refer to Exercise 4.85. Suppose the sampling of 3 alternators is done by randomly choosing one after another and without replacement. The event A can then be described as G 1 G2G3, where G denotes "good" and the suffixes refer to the order of the draws.

> A batch of 18 used automobile alternators contains 4 defectives. If 3 alternators are sampled at random, find the probability of the event (a) A = [ None of the defectives appear] (b) B = [ Exactly two defectives appear ]

> The following is a stem-and-leaf display with two-digit leaves. (The leading leaf digit = 10.0.) List the corresponding measurements.

> A local company is giving away five streaming devices to persons who visit its website and register on a specified day. Each person is allowed to register three times for the drawing. If, at the time of drawing, there are 6200 entries, what is the probab

> After a preliminary screening, the list of qualified jurors consists of 10 males and 7 females. The 5 jurors the judge selects from this list are all males. Did the selection process seem to discriminate against females? Answer this by computing the prob

> Out of 12 people applying for an assembly job, 3 cannot do the work. Suppose two persons will be hired . (a) How many distinct p airs are possible? (b) In how many of the pairs will O or 1 person not be able to do the work? (c) If two persons are chos

> A psych ologist will select 5 preschool children from a class of 11 students in order to try out new abuse awareness material. (a) How many different selections are possible? (b) Suppose 4 of the 11 children are males. If the 5 selected children were t

> If a coin is tossed 11 times, the outcome can be recorded as an 11-character sequence of H's and T's according to the results of the successive tosses. In h ow m any ways can there be 4 H's and 7 T's? (Put differently, in how many ways can one choose 4 p

> Consider the following experiment: A coin will be tossed twice. If both tosses show heads, the experiment will stop. If one head is obtained in the two tosses, the coin will be tossed one more time, and in the case of both tails in the two tosses, the co

> Of 10 available candidates for membership in a university committee, 6 are men and 4 are women. The committee is to consist of 4 persons. (a) How many different selections of the committee are possible? (b) H ow many selections are possible if the comm

> Evaluate: (a) (8 4) (b) (10 3) (c) (21 2) (d) (21 19) (e) (25 3) (f) (25 22)

> Refer to Example where a manufacturer had difficulty getting enough LED screens. Now suppose, because of the shortage, the manufacturer had to obtain 30% of the screens from the second supplier and 15% from the third supplier. Find the (a) Probability

> A cable TV provider assigns 80% of its service calls to an independent contractor and 9% of these calls result in consumer complaints. The other 20% of the service calls are made by the companies' own employees, and these result in a 4% complaint rate. F

> A federal government study of the oil reserves in Elk Hills, CA, included a study of the amount of iron present in the oil. Make a stem-and-leaf display.

> At one automated international airport arrival location, facial identification software compares a camera image of the traveler with a scan of their passport picture. The procedure correctly concludes a match with 99.4% of males and 98.8% of females. The

> Refer to Example concerning spam but now suppose that a new list is available. Among the 1000 messages, the 350 spam messages have 310 that contain words on this list and the 650 normal messages have 70 that contain words on the list. (a) Obtain the pro

> In a county, men constitute 60% of the labor force. The rates of unemployment are 5.1 % and 4.3% among males and females, respectively. (a) In the context, of selecting a worker at random from the country labor force, state what probabilities the forego

> Carol and Karl both solve difficult computer problems that come to the student desk. Carol makes 60% of the repairs and Karl 40%. However, Carol's repairs are incomplete 4% of the time and Karl's are incomplete 6% of the time. (a) Determine the probabil

> Repeat Example 20 but change P(A I B) to .03. Data from Example 20: A is the event that a person tests positive for a serious virus and B is the event that the person actually has the virus. Suppose a person tests positive. Use Bayes' Theorem to update

> Consider tossing two fair coins and the events A: Head in the first toss B: Head in the second toss C: Both heads or both tails in the two tosses (a) Verify that the property of independence holds for all event pairs. (b) Show that P (ABC) is different f

> Bob, John, Linda, and Sue are the finalists in the campus bowling tournament. The winner and the first runner-up will be sent to a statewide competition. (a) List the sample space concerning the outcomes of the local tournament. (b) Give the compositio

> Of the patients reporting to a clinic with the symptoms of sore throat and fever, 25% have strep throat, 40% have an allergy, and 10% have both. (a) What is the probability that a patient selected at random has strep throat, an allergy, or both? (b) Are

> Refer to Exercise 4.48. Given that a landfill selected at random is found to have a high concentration of mercury, what is the probability that its concentration is: (a) High in barium? (b) Low in both arsenic and barium? ( c) High in either arsenic or b

> In 80% of the cases an electronic scanner is successful in detecting flaws in a material specimen. Three material specimens containing flaws will be tested with the scanner. Assume that the tests are independent. (a) List the sample space and assign pro

> The following data represent the scores of 40 students on a college qualification test (courtesy of R. W. Johnson). Make a stem-and-leaf display.

> An accountant screens large batches of bills according to the following sampling inspection plan. She inspects 4 bills chosen at random from each batch and p asses the batch if, among the 4, none is irregular. Find the probability that a batch will be pa

> Approximately 40% of the Wisconsin population have type 0 blood. If 4 persons are selected at random to be donors, find P [ at least one type O ] .

> Of three events, A, B, and C, suppose events A and B are independent and events B and C are mutually exclusive. Their probabilities are P(A) = .6, P(B) = .3, and P( C ) = .2. Express the following events in set notation and calculate their probabilities.

> A restaurant critic goes to a place twice. If she has an unsatisfactory experience during both visits, she will go once more. Otherwise she will make only the two visits. Assuming that the results for different visits are independent and that the probabi

> Of 20 rats in a cage, 12 are males and 9 are infected with a virus that causes hemorrhagic fever. Of the 12 male rats, 7 are infected with the virus. One rat is randomly selected from the cage. (a) If the selected rat is found to be infected, what is the

> Refer to Exercise 4.45. (a) If a fast food restaurant selected at random is found to comply with safety standards, what is the probability that it violates sanitary standards? (b) If a restaurant selected at random is found to violate at least one of t

> Suppose P(A) = .6andP(B) = .22. (a) Determine P ( A U B ) if A and B are independent. (b) Determine P ( A U B) if A and B are mutually exclusive. (c) Find P ( A I B) if A and B are mutually exclusive.

> When bidding on two projects, the president and vice president of a construction company make the following probability assessments for winning the contracts. For both cases, examine whether or not the probability assignment is permissible.

> If the probability of running out of gas is .03 and the probability the electronic starting system will not work is .01, (a) What is the probability that there will be enough gas and that the starting system will work? Assume the two events are independ

> An insurance company's records of 12,299 automobile insurance policies revealed that 2073 made a claim. Among insured drivers under age 25, there were 1032 claims out of 5192 policies (courtesy of J. Hickman). Assuming the claim history is valid for the

> Referring to Exercise 2.20, construct a density histogram using the intervals (6.5, 6.7], (6.7, 6.9], (6.9, 7.1], (7.1, 7.5], and (7.5, 7.9]. Using R: With the observations in x hist(x,breaks= c(6.5,6. 7,6.9, 7.1, 7.5, 7 .9),prob=T) Data from Exercise 2

> One type of passenger airplane has four engines but it can still fly with only one. Suppose each engine has probability .002 of failing during a flight. (a) Calculate the probability of all four engines failing during the same flight. Assume independenc

> An urn contains two green balls and three red balls. Suppose two balls will be drawn at random one after another and without replacement (i.e., the first ball drawn is not returned to the urn before the second one is drawn). (a) Find the probabilities o

> Records of student patients at a dentist's office concerning fear of visiting the dentist suggest the following proportions. For a student selected at random, consider the events A = [ Fear ] M = [ Middle school ] (a) Find the probabilities P(A) P(AM

> For two events A and B, the following probabilities are given. P(A) = .35 P(B) = .30 P(A | B) = .6 Use the appropriate laws of probability to calculate (a) P(A¯) (b) P( AB ) (c) P(A U B)

> A witness identified a suspect as having blond hair. However, when tested under lighting conditions similar to those on the night of the incident, it was concluded that the probability of correctly identifying blond h air is .80 and the probability of be

> Th e following data relate to the proportions in a population of drivers. A = Defensive driver training last year B = Accident in current year The probabilities are given in the accompanying Venn diagram. Find P( B I A ). Are A and B independent?

> Refer to Exercise 4.39. Find (a) The conditional probability that B occurs given that A occurs. (b) The conditional probability that B does not occur given that A occurs. (c) The conditional prob ability that B occurs given that A does not occur. Dat

> A person is randomly selected from persons working in your state. Consider the two events A = [Lawyer] B = [ Driving a new luxury car ] Given that the person selected drives a new luxury car, would you expect the probability of A to be larger, the same,