For the curve f(x) graphed in Exercise 6.1(c), which of the two intervals [ 0 < X < .5] or [ 1.5 < X < 2] is assigned a higher probability?
> Referring to Example, where the 158 times to complete the firefighter test have mean 307. 77 and standard deviation 51.852, obtain a 99% confidence interval for the mean time of all possible recruits who would complete the test.
> A researcher asked participants to wear a simple counting device for a week and they counted the number of times that they thought about food. Determine a point estimate of the daily mean number of times a person thinks about food and the (1 - a)% error
> The freshness of produce at a superstore is rated on a scale of 1 to 5 with 5 being very fresh . From a random sample of 49 customers, the average score was 3.8 with a standard deviation of .7. (a) Obtain a 95% confidence interval for the population mean
> Students are asked about the number of songs they downloaded from a pay-for-songs Web site the last month. From a random sample of 39 students, the sample mean was 4. 7 with a standard deviation of 3.2. (a) Obtain a 95% confidence interval forµ, the mea
> Refer to Exercise 5.7. Suppose that for each purchase P(B) = ½ and the decisions in different weeks are independent. Assign probabilities to the elementary outcomes and obtain the distribution of X. Data from Exercise 5.7: Each week a grocery shopper bu
> In a study designed to find differences in personality between cat and dog lovers, 3 subjects were first classified according to their answers to a questionnaire about attitudes towards pets, and previous pet ownership. The n = 66 subjects classified as
> In a study on the nutritional qualities of fast foods, the amount of fat was measured for a random sample of 35 hamburgers of a p articular restaurant chain. The sample mean and standard deviation were found to be 30 .2 and 3.8 grams, respectively. Use t
> A nutritionist records the time to eat an evening meal, at a student cafeteria, for 64 students. She obtains x = 36.2 and s = 5.6 minutes and reports that the 95% confidence interval for the mean time to eat is or (30.79, 41.6 1) (a) Is this statement c
> Each day of the year, a large sample of cellular phone calls is selected and a 95% confidence interval is calculated for the mean length of all cellular phone calls on that day. Of these 365 confidence intervals, one for each day of the year, approximate
> A company wants to check the consistency of electronic copies of signatures for consumer credit purchases. A sample of 49 electronic signatures are available from the same customer. One measure of consistency in signing is the total length that the scrip
> Table records the number of items returned by 30 persons to a large discount department store in late December. The summary statistics are n = 30, x = 2.538, s = 1.303 Obtain a 98% confidence interval for µ, the population mean number of items returned
> To estimate µ with a 90% error margin of 2.9 units, one has determined that the required sample size is 108. What then is the required sample size if one wants the 95% error margin to be 1.8 units?
> Referring to Exercise 8.4, suppose that the survey of 50 contested items was, in fact, a pilot study intended to give an idea of the population standard deviation. Assuming ( = $25, determine the sample size that is needed for estimating the population m
> A researcher wants to estimate µ, the mean number of minutes before a person scores over 200 on a new computer game. She wishes to get estimates, separately, for each of the groups (a) novices, (b) occasional game players, and ( c) expert game players. W
> Find the standardized variable Z if X has (a) Mean 13 and standard deviation 3. (b) Mean 57 and standard deviation 16. (c) Mean 142 and variance 36.
> The probability distribution of X is given by the function for x = 0, 1, 2, 3 Find (a) P [ X = 1 ] (b) P [ X is odd ].
> Which of the distributions in Figure 3 are compatible with the following statements? (a) The first test was too easy because over half the class scored above the mean. (b) In spite of recent large increases in salary, half of the professional football
> If a student is more likely to be late than on time for the 1:20 PM history class: (a) Determine if the median of the student's arrival time distribution is earlier than, equal to, or later than 1:20 PM. (b) On the basis of the given information, can yo
> Determine the 15th percentile of the curve in Exercise 6.1. Data from Exercise 6.1: Which of the functions sketched below could be a probability density function for a continuous random variable? Why or why not?
> Refer to the volume of timber data. (a) Make a normal-scores plot of the original data. (b) Make a normal-scores plot of the fourth root of the data. (c) Compare the two plots and comment.
> The MINITAB computer language makes it possible to easily transform data. With the data already set in column 1 , the commands will place the natural logarithm loge x in C2, √x in C3, and X1/4 in C4. Normal-scores plots can then be cons
> Use MINITAB or another package program to make a normal-scores plot of the lizards' speed test. Comment on the pattern.
> Use MINITAB or another package program to make a normal-scores plot of the College Qualification Test (CQT) data. Comment on the pattern.
> Use MINITAB or another package program to make a normal-scores plot of the malt extract data in the Data Bank.
> Determine the median and the quartiles for the curve depicted in Exercise 6.1. Data from Exercise 6.1: Which of the functions sketched below could be a probability density function for a continuous random variable? Why or why not?
> Use a computer program to make a normal-scores plot for the volume of timber data in Table 4. (Courtesy of Professor Alan Ek) Comment on the departure from normality displayed by the normal-scores plot. We illustrate a normal-scores plot using MINITAB. W
> For each case, list the values of X and f (x) and examine if the specification represents a probability distribution. If it does not, state what properties are violated. (a) f( x ) = 1/6 (x – 1) for x = 1, 2, 3, 4 (b) f( x ) = x – 2 for x = 0, 2, 4 (c) f
> Suppose that 20% of the trees in a forest are infested with a certain type of parasite. (a) What is the probability that, in a random sample of 300 trees, the number of trees having the parasite will be between 49 and 71 inclusive? (b) After sampling 3
> In a large midwestern university, 30% of the students live in apartments. If 200 students are randomly selected, find the probability that the number of them living in apartments will be between 55 and 70 inclusive.
> The weekly amount spent by a small company for in-state travel has approximately a normal distribution with mean $1450 and standard deviation $220. What is the probability that the actual expenses will exceed $1560 in 20 or more weeks during the next yea
> A survey reports that 96% of the people think that violence has increased in the past five years. Out of a random sample of 50 persons, 48 expressed the opinion that citizens have become more violent in the past five years. Does the normal approximation
> The unemployment rate in a city is 7.9%. A sample of 300 persons is selected from the labor force. Approximate the probability that (a) Less than 18 unemployed persons are in the sample. (b) More than 30 unemployed persons are in the sample.
> The median age of residents of the United States is 37.2 years. If a survey of 200 residents is taken, approximate the probability that at least 110 will be under 37.2 years of age.
> Copy Figure 16 and add the standard score scale Underneath the x-axis for n = 5, 12, 25. Notice how the distributions center on zero and most of the probability lies between z = -2 and z = 2.
> State whether or not the normal approximation to the binomial is appropriate in each of the following situations. (a) n = 90, p = .24 (b) n = 100, p = .03 (c) n= 120, p = .98 (d) n= 6 1, p = .40
> A recent study reported that 54% of the adults in the United States drink at least one cup of coffee a day. Suppose that this is still the current rate. What is the normal approximation to the probability that, in a random sample of 1000 adults, the numb
> Determine the median and the quartiles for the probability distribution depicted in Exercise 6.1(a). Data from Exercise 6.1: Which of the functions sketched below could be a probability density function for a continuous random variable? Why or why not?
> Examine if the following are legitimate probability distributions.
> A study by the National Endowment of the Arts revealed that 19.7% of adults age 18-24 played a musical instrument in the past 12 months. Suppose that is still the current rate. What is the normal approximation to the probability, that in a random sample
> Let the number of successes X have a binomial distribution with n = 20 and p = .5 (a) Find the exact probability of each of the following (b) Apply the normal approximation to each situation in part (a).
> Let the number of successes X have a binomial distribution with n = 25 and p = .6 (a) Find the exact probabilities of each of the following: (b) Apply the normal approximation to each situation in part (a).
> It is reasonable to model the distribution that produced the lizards' speed test as normal distribution with mean 1.7 mis and standard deviation .57 m is. Find the probability that the speed of a new lizard (a) Will exceed 2.5 m is. (b) Will be less th
> The time for an emergency medical squad to arrive at the sports center at the edge of town is distributed as a normal variable with µ = 17 minutes and ( = 3 minutes. (a) Determine the probability that the time to arrive is: (i) More than 22 minutes. (
> Suppose the contents of bottles of water coming off a production line have a normal distribution with mean 9.1 ounces and standard deviation .1 ounce. (a) If every bottle is labeled 9 ounces, what proportion of the bottles contain less than the labeled a
> Refer to Exercise 6. IO where, according to current U.S. Census Bureau data, the heights of 20- to 29-year-old women can be well approximated by a normal distribution with mean 64.1 inches and standard deviation 3.1 inches. (a) What is the probability t
> Th e diameter of hail hitting the ground during a storm is normally distributed with a mean of .5 inch and a standard deviation of .1 inch . What is the probability that: (a) A hailstone picked up at random will have a diameter greater than . 71 inch ?
> The weights of apples served at a restaurant are normally distributed with a mean of 5 ounces and standard deviation of 1.2 ounces. What is the probability that the next person served will be given an apple that weighs less than 4 ounces?
> Th e time it takes a symphony orchestra to play Beethoven's Ninth Symphony has a normal distribution with a mean of 64.3 minutes and a standard deviation of 1.15 minutes. The next time it is played, what is the probability that it will take between 62.5
> Let the random variable X represent the sum of the points in two tosses of a die. (a) List the possible values of X. (b) For each value of X, list the corresponding elementary outcomes. (c) Obtain the probability distribution of X .
> According to the children's growth chart that doctors use as a reference, the heights of two-year old boys are nearly normally distributed with a mean of 34.5 inches and a standard deviation of 1.4 inches. If a two-year-old boy is selected at random, wha
> It is reasonable to model the distribution that produced the College Qualification Test (CQT) data as a normal distribution with mean 150 and standard deviation 25.4. (a) What is the probability of a new student scoring above 195? (b) What score has prob
> Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 500 and a standard deviation of 100. Find the probability that a student will score: (a) Over 650. (b) Less than 250. (c) Between 325 and 675.
> Referring to Exercise 6.25, find b such that (a) P[ X < b] = .7995 (b) P [ X > b ] = .002 (c) P[X < b ] = .015 Data from Exercise 6.25: Data suggests that the normal distribution with mean 13.0 and standard deviation 2.4 is a plausible model for the
> Data suggests that the normal distribution with mean 13.0 and standard deviation 2.4 is a plausible model for the length (feet) of adult anaconda snakes. Find (a) P[X < 10.4 ] (b) P [ X ≤ 17.8 ] (c) P [ X > 17.8 ] (d) P[X > 16. 72 ] (e) P [10.24 ≤ X ≤ 1
> Find (a) P(Z. < .14) (b) The 14th percentile of Z. (c) P(Z < .86) (d) The 86th percentile of Z.
> Find (a) P [Z < .33 ]. (b) The 33rd percentile of the standard normal distribution. (c) P [Z < .97 ]. (d) The 97th percentile of the standard normal distribution.
> Find the quartiles of the standard normal distribution.
> Find the z value in each of the following cases . (a) P[Z < z ] = .1762 (b) P[Z > z ] = .10 (c) P[-z < Z < z ] = .954 (d) P[-.6 < Z < z ] = .50
> Refer to Exercise 5.9 but let X denote the maximum years’ experience among the two persons selected. (a) List all choices and the corresponding values of X. (b) List the distinct values of X . (c) Obtain the probability distribution of X. Data from E
> Identify each of the following as a discrete or continuous random variable. (a) Number of empty seats on a flight from Atlanta to London. (b) Yearly low temperature in your city. (c) The height of the highest wave on the north shore of Hawaii next winter
> On flights from San Francisco to Chicago, the number of empty seats are to be grouped into the following classes: 0-4, 5- 9, 10- 14, 15- 19, more than 19. Is it possible to determine from this frequency distribution the exact number of flights on which t
> The weights of the players on the university football team (to the nearest pound) are to be grouped into the following classes: 160-175, 175-190, 190-205, 205-220, 220-235, 235 or more. The left endpoint is included but not the right endpoint. Explain wh
> Cities must find better ways to dispose of solid waste. According to the Environmental Protection Agency, in a recent year, the composition of solid municipal waste was (a) Determine the percentage of other materials in the solid waste. This category inc
> Make a control chart for the extraordinary event overtime data in Example 23 after removing the outlier identified in that example. You need to recalculate the mean and standard deviation.
> Make a control chart for the data in Exercise 2.93 and comment. Data from Exercise 2.93: A city department has introduced a quality improvement program and has allowed employees to get credit for overtime hours when attending meetings of their quality g
> Make a control chart for the data referred to in Exercise 2.92 and comment. Data from Exercise 2.92: Make a time plot of the mail order phone call data in Exercise 2.48 and comment on the statistical control. Data from Exercise 2.48: A large mail-order
> A city department has introduced a quality improvement program and has allowed employees to get credit for overtime hours when attending meetings of their quality groups. The total number of overtime meeting hours for each of the 26 pay periods in one ye
> Make a time plot of the mail order phone call data in Exercise 2.48 and comment on the statistical control. Data from Exercise 2.48: A large mail-order firm employs numerous persons to take phone orders. Computers on which orders are entered also automa
> With reference to Exercise 2.90: (a) Calculate the median number of lost House seats. (b) Find the maximum and minimum losses and identify these with a president. (c) Det ermine the range for the number of House seats lost. Data from Exercise 2.90: P
> Presidents also take midterms1 After two years of the president's term, members of Congress are up for election. The following table gives the number of net seats lost, by the party of the president, in the House of Representatives starting from Eisenhow
> Which of the following are anecdotal and which are based on a sample? (a) Seventy-five text messages were sent one day during a lecture by students in a large class. (b) Erik says he gets the best bargains at online auctions by bidding on items whose ter
> Refer to Exercise 2.3 and the data on extracurricular activities. Find the sample mean and standard deviation. Data from Exercise 2.3: A student at the University of Wisconsin surveyed 40 students in her dorm concerning their participation in extracurri
> Refer to the data on hours of sleep. (a) Obtain the five-number summary: minimum, Q1, Q2 , Q3, and maximum. (b) Make a boxplot of the hours of sleep.
> Referring to the earthquake data in Exercise 2.20, (a) Find the sample mean and standard deviation. (b) What proportion of these observations lies between x ± 2 s? Data from Exercise 2.20: In a recent year, 35 sites around the world expe
> Referring to the earthquake data in Exercise 2.20, (a) Obtain a five-number summary: minimum, Q1, Q2, Q3, maximum. (b) Construct a boxplot. Data from Exercise 2.20: In a recent year, 35 sites around the world experienced earthquakes of magnitude great
> Refer to the data on throwing speed in Exercise 2.42. Make separate boxplots to compare males and females. Data from Exercise 2.42: Physical education researchers interested in the development of the overarm throw measured the horizontal velocity of a t
> Two cities provided the following information on public school teachers' salaries. (a) Construct a boxplot for the salaries in City A. (b) Construct a boxplot, on the same graph, for the salaries in City B. (c) Are there larger differences at the lower
> The weights ( oz) of nineteen babies born in Madison Wisconsin are summarized in the computer output. Obtain the z score for a baby weighing (a) 102 oz (b) 144 oz
> z-value of a measurement = Measurement - x¯ / s When two measurements originate from different sources, converting them to the z scale helps to draw a sensible interpretation of their relative magnitudes. For instance, suppose a student scored 65 in a ma
> Refer to the data on number of returns. (a) Calculate x and s. (b) Find the proportions of the observations that are in the intervals x ± s, x ± 2 s, and x ± 3 s. (c) Compare the results of part (b) with the empirical guidelines.
> Refer to the data on lizards in Exercise 2.19. (a) Calculate x ands. (b) Find the proportion of the observations that are in the intervals x ± s, x ± 2 s, and x ± 3 s. (c) Compare the results of part (b) with
> Which of the following are anecdotal and which are based on a sample? (a) Ellie told her friends that she is saving $31 a month because she changed to a prepaid cell phone. (b) One morning, among a large number of coffee shop patrons, the orders of 47 c
> Refer to the data on bone mineral content in Exercise 2.41. (a) Calculate x ands. (b) Find the proportion of the observations that are in the intervals x ± s, x ± 2 s, and x ± 3 s. (c) Compare the results of p
> Calculations with the test scores data of Exercise 2.22 give x = 150.125 and s = 24.677. (a) Find the proportion of the observations in the intervals x ± 2 s and x ± 3 s. (b) Compare your findings in part (a) with those su
> Should you be surprised if the range is larger than twice the interquartile range? Explain.
> For the extracurricular data of Exercise 2.3, calculate the interquartile range. Data from Exercise 2.3: A student at the University of Wisconsin surveyed 40 students in her dorm concerning their participation in extracurricular activities during the pa
> For the data set of Exercise 2.22, calculate the interquartile range. Data from Exercise 2.22: The following data represent the scores of 40 students on a college qualification test (courtesy of R. W. Johnson).
> 1. If a fixed number c is added to all measurements in a data set, the deviations ( x - x¯) remain unchanged. Consequently, s2 and s remain unchanged. 2. If all measurements in a data set are multiplied by a fixed number d, the deviations ( x - x) get
> The weights (oz) of nineteen babies born in Madison, Wisconsin, are summarized in the computer output. (a) Locate a measure of variation and also calculate the sample variance. (b) Calculate the interquartile range and interpret this value. (c) Give a v
> The monthly number of hours students spend doing community service are summarized in the computer output: (a) Locate a measure of variation and also calculate the sample variance. (b) Calculate the interquartile range and interpret this value. (c) Give
> The performance time (minutes) for Beethoven's Ninth Symphony is obtained from each of seven compact discs. 66.9 66.2 71.0 68.6 65.4 68.4 71.9 (a) Find the sample median. (b) Find the sample mean . (c) Find the sample standard deviation. (d) Use soft
> With reference to checked bags in Exercise 2.13, (a) Find the sample mean . (b) Find the sample standard deviation. Data from Exercise 2.13: A sample of 50 departing airline passengers at the main check-in counter produced the following number of bags
> About 42% of the members of a local hiking club own a dog. Should these people be considered as a random sample of dog ownership for persons living in the city7
> With reference to the data on the length of 10 major league baseball games in Exercise 2.43: (a) Find the sample mean. (b) Find the sample variance. (c) Find the sample standard deviation. Data from Exercise 2.43: On opening day one season, 10 major
> With reference to the radiation leakage data given in Exercise 2.15, calculate : (a) The sample variance. (b) The sample standard deviation. Data from Exercise 2.15: Before microwave ovens are sold, the manufacturer must check to ensure that the radia
> Refer to Exercise 12.16. The estimated standard errors of β1 and β2 are .0606 and .0632, respectively. (a) Obtain a 90% confidence interval for β1. (b) Test H0 : β2 = .5 versus H1 : β1 ≠ .5 with .05. Data from Exercise 12.16: Some researchers illust
> Some researchers illustrate a multiple linear regression equation to predict the yearly output of an oil field. We use their latest 20 years of data and change the units of three of their variables to y = loge (yearly output) where output is measured in
> Consider the data on a response variable and two predictor variables. (a) Fit a multiple regression model with response variable y. (b) Verify your answer using software.
> A genetic experiment is undertaken to study the competition between two types of female flies (Drosophila melanogaster) in cages with one male genotype acting as a substrate. The independent variable x is the time spent in cages, and the dependent variab
> An environmental scientist identified a point source for E. Coli at the edge of a stream. She then measured y = E. Coli, in colony forming units per I 00 ml of water, at different distances, in feet, downstream from the point source. Suppose she obtains
