New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
business
statistics principles and methods
Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+c. What is the probability that the duration of pregnancy is within 16 days of the mean duration?
=+b. What is the probability that the duration of pregnancy is at most 240 days?
=+a. What is the probability that the duration of pregnancy is between 250 and 300 days?
=+7.51 Let x denote the duration of a randomly selected pregnancy (the time elapsed between conception and birth). Accepted values for the mean value and standard deviation of x are 266 days and 16 days, respectively. Suppose that a normal distribution is an appropriate model for the probability
=+7.50 The light bulbs used to provide exterior lighting for a large office building have an average lifetime of 700 hr. If the distribution of the variable x 5 length of bulb life can be modeled as a normal distribution with a standard deviation of 50 hr, how often should all the bulbs be
=+d. Describe the largest 5% of the pH distribution.
=+c. What is the probability that the resulting pH is at most 5.95?
=+b. What is the probability that the resulting pH exceeds 6.10?
=+a. What is the probability that the resulting pH is between 5.90 and 6.15?
=+7.49 Suppose that the distribution of pH readings for soil samples taken in a certain geographic region can be approximated by a normal distribution with mean 6.00 and standard deviation 0.10. The pH of a randomly selected soil sample from this region is to be determined.
=+7.48 Your statistics professor tells you that the distribution of scores on a midterm exam was approximately normal with a mean of 78 and a standard deviation of 7. The top 15% of all scores have been designated A’s. Your score was 89. Did you receive an A? Explain.
=+b. What proportion of adult women would be excluded from employment because of the height restriction?
=+a. Is the claim that 94% of all women are shorter than 5 ft 7 in. correct?
=+7.47 The Wall Street Journal (February 15, 1972) reported that General Electric was being sued in Texas for sex discrimination because of a minimum height requirement of 5 ft 7 in. The suit claimed that this restriction eliminated more than 94% of adult females from consideration. Let x represent
=+e. Describe the most extreme 10% of the moisture loss distribution. (Hint: The most extreme 10% consists of the largest 5% and the smallest 5%.)
=+d. Describe the largest 10% of the moisture loss distribution.
=+c. What is the probability that x is at least 7%?
=+b. What is the probability that x is at most 4.0%?
=+a. What is the probability that x is between 3.0% and 5.0%?
=+7.46 Accurate labeling of packaged meat is difficult because of weight decrease resulting from moisture loss(defined as a percentage of the package’s original net weight). Suppose that the normal distribution with mean value 4.0% and standard deviation 1.0% is a reasonable model for the
=+7.45 A machine producing vitamin E capsules operates in such a way that the distribution of x 5 actual amount of vitamin E in a capsule can be modeled by a normal curve with mean 5 mg and standard deviation 0.05 mg. What is the probability that a randomly selected capsule contains less than 4.9
=+4. Combine the observations from your group with those from the other groups. Use the resulting data to approximate the distribution of x. Comment on the resulting distribution in the context of the risk of salmonella exposure if the manager’s proposed procedure is use
=+f. Repeat Steps (b)–(d) at least 10 times, each time recording the observed x value.
=+e. Replace all slips, so that the bag now contains all 12 “eggs.”
=+d. Note the number of bad eggs among the four selected.(This is an observed x value.)
=+c. Mix the remaining slips and select four “eggs” from the bag.
=+b. Mix the slips and then select three at random and remove them from the bag.
=+a. Take 12 identical slips of paper and write “Good” on 9 of them and “Bad” on the remaining 3. Place the slips of paper in a paper bag or some other container.
=+3. Suppose that a carton of one dozen eggs does happen to have exactly three eggs that carry salmonella and that the manager does as he proposes: selects three eggs at random and throws them out, then uses the remaining nine eggs in four-egg quiches. Let x 5 number of eggs that carry salmonella
=+2. Suppose the following argument is made for three-egg quiches rather than four-egg quiches: Let x 5 number of eggs that carry salmonella. Then p(0) 5 P(x 5 0) 5 (.75)3 5 .422 for three-egg quiches and p(0) 5 P(x 5 0) 5 (.75)4 5 .316 for four-egg quiches. What assumption must be made to justify
=+1. Working in a group or as a class, discuss the folly of the above statement!
=+Background: The Salt Lake Tribune (October 11, 2002)printed the following account of an exchange between a restaurant manager and a health inspector:The recipe calls for four fresh eggs for each quiche. A Salt Lake County Health Department inspector paid a visit recently and pointed out that
=+A large number of topsoil samples were analyzed for manganese (Mn), zinc (Zn), and copper (Cu), and the resulting data were summarized using histograms. The investigators transformed each data set using logarithms in an effort to obtain more symmetric distributions of values. Do you think the
=+Research [1984]: 207–217):1 1original value 0.5 1.0 1.5 2.0 10 20 30 Cu Untransformed data−0.6 0.0 Cu Log-transformed data Number of samples 0.5 1.0 1.5 2.0 10 20 30 Zn Number of samples−0.6 0.0
=+7.44 The following figure appeared in the paper “EDTAExtractable Copper, Zinc, and Manganese in Soils of the Canterbury Plains” (New Zealand Journal of Agricultural
=+1===+d. Consider transformed value 5 and construct a histogram of the transformed data. Does it appear to resemble a normal curve?
=+c. Use a calculator or statistical computer package to calculate logarithms of these observations and construct a histogram. Is the logarithmic transformation satisfactory?
=+b. Draw a histogram based on the class intervals 5 to ,10, 10 to ,15, 15 to ,20, 20 to ,25, 25 to ,30, 30 to ,40, 40 to ,50, 50 to ,100, and 100 to ,500.Is a transformation of the data desirable? Explain.
=+a. Construct a stem-and-leaf display in which 448.0 is shown beside the display as an outlier value, the stem of an observation is the tens digit, the leaf is the ones digit, and the tenths digit is suppressed (e.g., 21.5 has stem 2 and leaf 1). What do you perceive as the most prominent feature
=+7.43 ● Ecologists have long been interested in factors that might explain how far north or south particular animal species are found. As part of one such study, the paper“Temperature and the Northern Distributions of Wintering Birds” (Ecology [1991]: 2274–2285) gave the following body
=+b. Does the square-root transformation result in a histogram that is more symmetric than that of the original data? (Be careful! This one is a bit tricky because you don’t have the raw data; transforming the endpoints of the class intervals results in class intervals that are not necessarily
=+a. Draw a histogram for this frequency distribution.Would you describe the histogram as positively or negatively skewed?
=+7.42 ● The article “The Distribution of Buying Frequency Rates” (Journal of Marketing Research [1980]: 210–216)reported the results of a study of dentifrice purchases.The investigators conducted their research using a national sample of 2071 households and recorded the number of
=+c. Find a transformation for these data that results in a more symmetric histogram than what you obtained in Part (b).
=+b. Draw the histogram corresponding to the frequency distribution in Part (a). How would you describe the shape of this histogram?
=+a. Construct a frequency distribution using the class intervals 0 to ,100, 100 to ,200, and so on.
=+7.41 ● In a study of warp breakage during the weaving of fabric (Technometrics [1982]: 59–65), 100 pieces of yarn were tested. The number of cycles of strain to breakage was recorded for each yarn sample. The resulting data are given in the following table:86 146 251 653 98 249 400 292 131
=+c. Would you recommend transforming the data? Explain.
=+b. Would you describe this histogram as having a positive or a negative skew?
=+a. Construct a relative frequency distribution for this data set, and draw the corresponding histogram.
=+7.40 ● The following data are a sample of survival times(in days from diagnosis) for patients suffering from chronic leukemia of a certain type (Statistical Methodology for Survival Time Studies, Bethesda, MD: National Cancer Institute, 1986):7 47 58 74 177 232 273 285 317 429 440 445 455 468
=+Construct a histogram of the transformed data. Compare your histogram to those given in Figure 7.33. Which of the cube-root and the square-root transformations appears to result in the more symmetric histogram(s)?
=+symmetric than the distribution of the original data.Another transformation that has been suggested by meteorologists is the cube root: transformed value 5 (original value)1/3. The original values and their cube roots (the transformed values) are given in the following table:Original Transformed
=+7.39 ● Example 7.19 examined rainfall data for Minneapolis–St. Paul. The square-root transformation was used to obtain a distribution of values that was more
=+The 13 largest normal scores for a sample of size 25 are 1.965, 1.524, 1.263, 1.067, 0.905, 0.764, 0.637, 0.519, 0.409, 0.303, 0.200, 0.100, and 0. The 12 smallest scores result from placing a negative sign in front of each of the given nonzero scores. Construct a normal probability plot.Does it
=+7.38 ● Consider the following sample of 25 observations on the diameter x (in centimeters) of a disk used in a certain system.16.01 16.08 16.13 15.94 16.05 16.27 15.89 15.84 15.95 16.10 15.92 16.04 15.82 16.15 16.06 15.66 15.78 15.99 16.29 16.15 16.19 16.22 16.07 16.13 16.11
=+7.37 ● The following observations are DDT concentrations in the blood of 20 people:24 26 30 35 35 38 39 40 40 41 42 52 56 58 61 75 79 88 102 42 Use the normal scores from Exercise 7.36 to construct a normal probability plot, and comment on the appropriateness of a normal probability model.
=+7.36 ● The paper “The Load-Life Relationship for M50 Bearings with Silicon Nitride Ceramic Balls” (Lubrication Engineering [1984]: 153–159) reported the following data on bearing load life (in millions of revolutions); the corresponding normal scores are also given:x Normal Score x
=+7.35 ● Consider the following 10 observations on the lifetime (in hours) for a certain type of component:152.7 172.0 172.5 173.3 193.0 204.7 216.5 234.9 262.6 422.6 Construct a normal probability plot, and comment on the plausibility of a normal distribution as a model for component lifetime.
=+The variable under study was the amount of cadmium in North Atlantic scallops. Do the sample data suggest that the cadmium concentration distribution is not normal? Explain.
=+7.34 The following normal probability plot was constructed using part of the data appearing in the paper“Trace Metals in Sea Scallops” (Environmental Concentration and Toxicology 19: 1326–1334):++-----+-----+-----+-----+-----+-1.60 -0.80 0.00 0.80 1.60 2.40 Obse Normal score* * * * ***
=+Based on the plot, do you think it is reasonable to assume that the normal distribution provides an adequate description of the steam rate distribution? Explain.
=+7.33 Ten measurements of the steam rate (in pounds per hour) of a distillation tower were used to construct the following normal probability plot (“A Self-Descaling Distillation Tower,” Chemical Engineering Process[1968]: 79–84):+++++-----+-----+-----+-----+-----+-1.60 -0.80 0.00 0.80 1.60
=+c. How much time is required for the fastest 25% of all students to complete the exam?
=+b. How much time should be allowed for the exam if we wanted 90% of the students taking the test to be able to finish in the allotted time?
=+a. If 50 min is allowed for the exam, what proportion of students at this university would be unable to finish in the allotted time?
=+7.32 Consider the variable x 5 time required for a college student to complete a standardized exam. Suppose that for the population of students at a particular university, the distribution of x is well approximated by a normal curve with mean 45 min and standard deviation 5 min.
=+e. Suppose that special training is to be made available to the slowest 20% of the typists. What typing speeds would qualify individuals for this training?
=+What is the probability that both their typing rates exceed 75 wpm?
=+d. Suppose that two typists are independently selected.
=+c. Would you be surprised to find a typist in this population whose net rate exceeded 105 wpm? (Note: The largest net rate in a sample described in the paper cited is 104 wpm.)
=+b. What is the probability that a randomly selected typist’s net rate is between 45 and 90 wpm?
=+a. What is the probability that a randomly selected typist’s net rate is at most 60 wpm? less than 60 wpm?
=+7.31 ▼ Suppose that the distribution of net typing rate in words per minute (wpm) for experienced typists can be approximated by a normal curve with mean 60 wpm and standard deviation 15 wpm. The paper “Effects of Age and Skill in Typing” (Journal of Experimental Psychology[1984]:
=+7.30 A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 in. A bearing is acceptable if its diameter is within 0.004 in. of this target value. Suppose, however, that the setting has changed during the course of
=+7.29 ▼ The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 120 sec and a standard deviation of 20 sec. The fastest 10% are to be given advanced training. What task times
=+c. If two such tanks are independently selected, what is the probability that both tanks hold at most 15 gal?
=+b. What is the probability that a randomly selected tank will hold between 14.7 and 15.1 gal?
=+a. What is the probability that a randomly selected tank will hold at most 14.8 gal?
=+7.28 A gasoline tank for a certain car is designed to hold 15 gal of gas. Suppose that the variable x 5 actual capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean 15.0 gal and standard deviation 0.1 gal.
=+7.27 Refer to Exercise 7.26. Suppose that there are two machines available for cutting corks. The machine described in the preceding problem produces corks with diameters that are approximately normally distributed with mean 3 cm and standard deviation 0.1 cm. The second machine produces corks
=+7.26 A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 3 cm and standard deviation 0.1 cm. The specifications call for corks with diameters between 2.9 and 3.1 cm.
=+e. If x is a variable with a normal distribution and a is a numerical constant (a Þ 0), then y 5 ax also has a normal distribution. Use this formula to determine the distribution of birth weight expressed in pounds (shape, mean, and standard deviation), and then recalculate the probability from
=+d. How would you characterize the most extreme 0.1% of all birth weights?
=+c. What is the probability that the birth weight of a randomly selected baby of this type exceeds 7 lb?(Hint: 1 lb 5 453.59 g.)
=+b. What is the probability that the birth weight of a randomly selected baby of this type is either less than 2000 g or greater than 5000 g?
=+a. What is the probability that the birth weight of a randomly selected baby of this type exceeds 4000 g? is between 3000 and 4000 g?
=+American Statistician [1999]: 298–302). (The investigators who wrote the article analyzed data from a particular year. For a sensible choice of class intervals, the histogram did not look at all normal, but after further investigations the researchers determined that this was due to some
=+7.25 Consider babies born in the “normal” range of 37–43 weeks gestational age. Extensive data support the assumption that for such babies born in the United States, birth weight is normally distributed with mean 3432 g and standard deviation 482 g (“Are Babies Normal,” The
=+7.24 Consider the population of all 1-gal cans of dusty rose paint manufactured by a particular paint company.Suppose that a normal distribution with mean m 5 5 ml and standard deviation s 5 0.2 ml is a reasonable model for the distribution of the variable x 5 amount of red dye in the paint
=+e. What is the relationship between the 70th z percentile and the 30th z percentile?
=+7.23 Because P(z , 0.44) 5 .67, 67% of all z values are less than 0.44, and 0.44 is the 67th percentile of the standard normal distribution. Determine the value of each of the following percentiles for the standard normal distribution (Hint: If the cumulative area that you must look for does
=+c. z* and 2z* separate the middle 98% of all z values from the most extreme 2%d. z* and 2z* separate the middle 92% of all z values from the most extreme 8%
=+7.22 Determine the value of z* such thata. z* and 2z* separate the middle 95% of all z values from the most extreme 5%b. z* and 2z* separate the middle 90% of all z values from the most extreme 10%
=+d. Separates the smallest 10% of all z values from the others
=+c. Separates the smallest 4% of all z values from the others
=+7.21 Determine the value z* thata. Separates the largest 3% of all z values from the othersb. Separates the largest 1% of all z values from the others
=+7.20 Let z denote a variable that has a standard normal distribution. Determine the value z* to satisfy the following conditions:a. P(z , z*) 5 .025b. P(z , z*) 5 .01c. P(z , z*) 5 .05d. P(z . z*) 5 .02e. P(z . z*) 5 .01f. P(z . z* or z , 2z*) 5 .20
=+7.19 Let z denote a variable having a normal distribution with m 5 0 and s 5 1. Determine each of the following probabilities:a. P(z , 0.10)b. P(z , 20.10)c. P(0.40 , z , 0.85)d. P(20.85 , z , 20.40)e. P(20.40 , z , 0.85)f. P(z . 21.25)g. P(z , 21.50 or z . 2.50)
=+7.18 Let z denote a variable that has a standard normal distribution. Determine each of the following probabilities:a. P(z , 2.36)b. P(z # 2.36)c. P(z , 21.23)d. P(1.14 , z , 3.35)e. P(20.77 # z # 20.55)f. P(z . 2)g. P(z $ 23.38) h. P(z , 4.98)
Showing 2900 - 3000
of 6202
First
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
Last
Step by Step Answers
Get 50% OFF
Claim Now
