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Questions and Answers of Statistics

Many cities sponsor marathons each year. The following histogram shows the distribution of times that it took for 10,002 runners to complete the Rome marathon in 2008, with a normal curve
The brain weights of a certain population of adult Swedish males follow approximately a normal distribution with mean 1,400 gm and standard deviation 100 gm. What percentage of the brain weights
Let Y represent a brain weight randomly chosen from the population of Exercise 4.3.3. Find(a) Pr{Y ≤ 1,325}(b) Pr{1,475 ≤ Y ≤ 1,600}Exercise 4.3.3The brain weights of a certain population of
In an agricultural experiment, a large uniform field was planted with a single variety of wheat. The field was divided into many plots (each plot being 7 × 100 ft) and the yield (lb) of grain was
Find the z-values corresponding to the following percentiles of the standard normal distribution. (a) The 75th percentile (b) The 90th percentile (c) The 95th percentile (d) The 99th percentile
For the wheat-yield distribution of Exercise 4.3.5, find (a) The 65th percentile (b) The 35th percentile Exercise 4.3.5 In an agricultural experiment, a large uniform field was planted with a single
The serum cholesterol levels of 12- to 14-year-olds follow a normal distribution with mean 155 mg/dl and standard deviation 27 mg/dl. What percentage of 12 to 14-year-olds have serum cholesterol
In Example 4.1.2 it was stated that bill length in a population of Blue Jays follow a normal distribution with mean µ = 25.4 mm and standard deviation σ = 0.8 mm. Use the 68%-95%-99.7% rule to
The following three normal quantile plots, (a), (b), and (c), were generated from the distributions shown by histograms I, II, and III. Which normal quantile plot goes with which histogram? How do
For each of the following normal quantile plots, sketch the corresponding histogram of the data.
The mean daily rainfall between January 1, 2007, through January 1, 2009, at Pismo Beach, California, was 0.02 inches with a standard deviation of 0.11 inches. Based on this information, do you think
The mean February 1 daily high temperature in Juneau, Alaska, between 1945 and 2005 was 1.1 °C with a standard deviation of 1.9oC. (a) Based on this information, do you think it is reasonable to
The following normal quantile plot was created from the times that it took 166 bicycle riders to complete the stage 11 time trial, from Grenoble to Chamrousse, France, in the 2001 Tour de France
The P-values for the Shapiro-Wilk test for the data appearing in quantile plots (a) and (b) are 0.235 and 0.00015. Which P-value corresponds to which plot? What is the basis for your decision?
(a) Trie P-value for the Shapiro-Wilk test of normality for the data in Exercise 4.4.3(b) is 0.039. Using this value to justify your answer, does it seem reasonable to believe that these data came
The activity of a certain enzyme is measured by counting emissions from a radioactively labeled molecule. For a given tissue specimen, the counts in consecutive 10-second time periods may be regarded
For the distribution of interspike-time intervals described in Exercise 4.S.9, find the quartiles and the interquartile range. Exercise 4.S.9 In the nerve-cell activity of a certain individual fly,
Among American women aged 20 to 29 years, 10% are less than 60.8 inches tall, 80% are between 60.8 and 67.6 inches tall, and 10% are more than 67.6 inches tall. Assuming that the height distribution
The intelligence quotient (IQ) score, as measured by the Stanford-Binet IQ test, is normally distributed in a certain population of children. The mean IQ score is 100 points, and the standard
Refer to the IQ distribution of Exercise 4.S.12. Suppose five children are to be chosen at random from the population. Find the probability that exactly one of them will have an IQ score of 80 or
A certain assay for serum alanine aminotransferase (ALT) is rather imprecise. The results of repeated assays of a single specimen follow a normal distribution with mean equal to the true ALT
Resting heart rate was measured for a group of subjects; the subjects then drank 6 ounces of coffee. Ten minutes later their heart rates were measured again. The change in heart rate followed a
Refer to the heart rate distribution of Exercise 4.S.16. Suppose we take a random sample of size 400 from this distribution. How many observations do we expect to obtain that fall between 0 and
Refer to the heart rate distribution of Exercise 4.S.16. If we use the 1.5 × IQR rule, from Chapter 2, to identify outliers, how large would an observation need to be in order to be labeled an
The bill lengths of a population of male Blue Jays follow approximately a normal distribution with mean equal to 25.4 mm and standard deviation equal to 0.8 mm (as in Example 4.1.2). Find the 95th
It is claimed that the heart rates of Exercise 4.S.16 follow a normal distribution. If this is true, which of the following Shapiro-Wilk's test F-values for a random sample of 15 subjects are
The following four normal quantile plots, (a), (b), (e). and (d), were generated from the distributions shown by histograms I, II, and III and another histogram that is not shown. Which normal
The heights of a certain population of corn plants follow a normal distribution with mean 145 cm and standard deviation 22 cm. What percentage of the plant heights are(a) 100 cm or more?(b) 120 cm or
Suppose four plants are to be chosen at random from the corn plant population of Exercise 4.S.4. Find the probability that none of the four plants will be more than 150 cm tall. Exercise 4.S.4 The
Refer to the corn plant population of Exercise 4.S.4. Find the 90th percentile of the height distribution. Exercise 4.S.4 The heights of a certain population of corn plants follow a normal
For the corn plant population described in Exercise 4.S.4, find the quartiles and the inter-quartile range. Exercise 4.S.4 The heights of a certain population of corn plants follow a normal
Suppose a certain population of observations is normally distributed. (a) Find the value of z* such that 95% of the observations in the population are between - z* and + z* on the Z scale. (b) Find
In the nerve-cell activity of a certain individual fly, the time intervals between "spike" discharges follow approximately a normal distribution with mean 15.6 ms and standard deviation 0.4 ms (as in
Consider taking a random sample of size 3 from the knee replacement population of Example 5.1.3. What is the probability that the total cost for those in the sample will be greater than $125,000?
Consider taking a random sample of size 3 from the knee replacement population of Example 5.1.3. What is the probability that the total cost for those in the sample will be between $80,000 and
Consider taking a random sample of size 3 from the knee replacement population of Example 5.1.3. What is the probability that the mean cost for those in the sample will be between $30,000 and $45,000?
Consider taking a random sample of size 2 (rather than of size 3) from the knee replacement population of Example 5.1.3. (a) How many possible samples of size n = 2 are then and what are those
Consider a hypothetical population of dogs in which there are four possible weights, all of which are equally likely: 42, 48, 52, or 58 pounds. If a sample of size n = 2 is drawn from this
The basal diameter of a sea anemone is an indicator of its age. The density curve shown here represents the distribution of diameters in a certain large population of anemones: the population mean
In a certain population of fish, the lengths of the individual fish follow approximately a normal distribution with mean 54.0 mm and standard deviation 4.5 mm. 'e saw in Example 4.3.1 that in this
In Exercise 5.2.10, the answer to part (b) was larger than the answer to part (a). Argue that this must necessarily be true, no matter what the population mean id standard deviation might be.
Professor Smith conducted a class exercise in which students ran a computer program to generate random samples from a population that had a mean of 50 d a standard deviation of 9 mm. Each of Smith's
A certain assay for serum alanine aminotransfer ase (ALT) is rather imprecise. The results of repeated assays of a single specimen follow a normal distribution with mean equal to the ALT
Refer to the histogram in Exercise 5.2.15. Suppose that 100 random samples are taken from this population and the sample mean is calculated for each sample. If we were to make a histogram of the
Refer to the histogram in Exercise 5.2.15. Suppose that 100 random samples are taken from this population and the sample mean is calculated for each sample. If we were to make a histogram of the
A medical researcher measured systolic blood pressure in 100 middle-aged men.5 The results are displayed in the accompanying histogram; note that the distribution is rather skewed. According to the
The partial pressure of oxygen, PaO2, is a measure of the amount of oxygen in the blood. Assume that the distribution of PaO2 levels among newborns has an average of 38 (mm Hg) and a standard
The serum cholesterol levels of a population of 12-to 14-year-olds follow a normal distribution with mean 155 mg/dl and standard deviation 27 mg/dl (as in Example 4.1.1). (a) What percentage of the
Refer to Exercise 5.2.4. Suppose we take a random sample of sixteen 12- to 14-year-olds from the population. (a) What is the probability that the mean cholesterol value for the group will be between
An important indicator of lung function is forced expiratory volume (FEV), which is the volume of air that a person can expire in one second. Dr. Hernandez plans to measure FEV in a random sample of
Refer to Exercise 5.2.6. Assume that the population distribution of FEV is normal with standard deviation 400 ml. (a) Find Pr{E} if n = 15 and the population mean is 2,800 ml. (b) Find Pr{E} if n =
The heights of a certain population of corn plants follow a normal distribution with mean 145 cm and standard deviation 22 cm (as in Exercise 4.S.4).(a) What percentage of the plants are between 135
Refer to Example 5.3.3. In the sampling distribution of for n = 4 (Figure 5.3.4), approximately what is the area under (a) The first peak? (b) The second peak?
Refer to Example 5.3.3. Consider the sampling distribution of for n = 2 (which is not shown in Figure 5.3.4). (a) Make a rough sketch of the sampling distribution. How many peaks does it have? Show
Refer to Example 5.3.3. Consider the sampling distribution of for n = 1. Make a rough sketch of the sampling distribution. How many peaks does it have? Show the location (on the Y-axis) of each
Consider interviewing a random sample of n = 50 adults. Let P denote the proportion of the 50 sampled adults who drink coffee. If the population proportion of coffee drinkers is 0.80, what is the
A certain cross between sweet-pea plants will produce progeny that are either purple flowered or white flowered;11 the probability of a purple-flowered plant is p = Suppose n progeny are to be
Cytomegalovirus (CMV) is a (generally benign) virus that infects one-half of young adults.12 If a random sample of 10 young adults is taken, find the probability that between 30% and 40% (inclusive)
In a certain population of mussels (Mytilus edu-lis), 80% of the individuals are infected with an intestinal parasite.1 A marine biologist plans to examine 100 randomly chosen mussels from the
Refer to Exercise 5.4.12. Find the probability that 85% or more of the sampled mussels will be infected, using the normal approximation with the continuity correction. Exercise 5.4.12 In a certain
Refer to Exercise 5.4.12. Suppose that the biologist takes a random sample of size 50. Find the probability that fewer than 35 of the sampled mussels will be infected, using the normal
A fair coin is to be tossed 20 times. Find the probability that 10 of the tosses will fall heads and 10 will fall tails, (a) Using the binomial distribution formula. (b) Using the normal
In the United States, 44% of the population has type O blood. Suppose a random sample of 12 persons is taken. Find the probability that 6 of the persons will have type O blood (and 6 will not) (a)
Refer to Exercise 5.4.3. Find the probability that at most 6 of the persons will have type O blood by using the normal approximation (a) Without the continuity correction. (b) With the continuity
An epidemiologist is planning a study on the prevalence of oral contraceptive use in a certain population.9 She plans to choose a random sample of n women and to use the sample proportion of oral
In a study of how people make probability judgments, college students (with no background in probability or statistics) were asked the following question.10 A certain town is served by two hospitals.
Consider random sampling from a dichotomous population with p = 0.3, and let E be the event that is within ±0.05 of p. Use the normal approximation (without the continuity correction) to calculate
Refer to Exercise 5.4.7. Calculate Pr{£} for n = 40 (rather than 400) without the continuity correction. Exercise 5.4.7 Consider random sampling from a dichotomous population with p = 0.3, and let E
Refer to Exercise 5.4.7. Calculate Pr{E} for n = 40 (rather than 400) with the continuity correction. Exercise 5.4.7 Consider random sampling from a dichotomous population with p = 0.3, and let E be
In an agricultural experiment, a large field of wheat was divided into many plots (each plot being 7 × 100 ft) and the yield of grain was measured for each plot. These plot yields followed
Consider taking a random sample of size 25 from a population of plants, measuring the weight of each plant, and adding the weights to get a sample total. In the context of this setting, explain what
The skull breadths of a certain population of rodents follow a normal distribution with a standard deviation of 10 mm. Let be the mean skull breadth of a random sample of 64 individuals from this
Suppose that every day for 3 months Bill takes a random sample of 20 college students, records the number of calories they consume on that day, finds the average of the 20 observations, and adds the
Consider taking a random sample of size 14 from the population of students at a certain college and measuring the diastolic blood pressure each of the 14 students. In the context of this setting,
The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches.15 (a) If a man is chosen at random from the population, find the
Suppose a botanist grows many individually potted eggplants, all treated identically and arranged in groups of four pots on the greenhouse bench. After 30 days of growth, she measures the total leaf
Consider taking a random sample of size 25 from a population in which 42% of the people have type A blood. What is the probability that the sample proportion with type A blood will be greater than
The activity of a certain enzyme is measured by counting emissions from a radioactively labeled molecule. For a given tissue specimen, the counts in consecutive 10-second time periods may be regarded
Refer to Exercise 5.S.9. In reality, what factors would tend to invalidate the assumption that each litter can be regarded as a random sample from the same population? Exercise 5.S.9 In a certain lab
Precipitation, measured in inches, for the month of March in Minneapolis, Minnesota, was recorded for 25 consecutive years. The values ranged from 0.3 up to 4.7, with a mean of 1.7 and an SD of
For each of the following cases (a and b),(i) state whether the study should be observational or experimental and why.(ii) state whether blinding should be used. If the study should be run blind or
For each of the following situations state whether or not a binomial would be an appropriate probability model for the variable Y and explain why. (a) Seeds of the garden pea (Pisum sativum) are
One variable studied was the amount of thiocyanate (mg/L) in the blood after rats consumed raw or heated flaxseeds. (a) Is this variable numeric or categorical? (b) If numeric, is this variable
This study aims to determine whether or not heating flaxseeds before consumption can alter the amount of thiocyanate in the blood. Researchers fed 14 rats a diet consisting of 30% flaxseeds for 30
Suppose that the thiocyanate blood concentration in rats fed a normal diet (free of flaxseeds) follows a normal distribution with population mean concentration of 53.3 mg/L and standard deviation of
The following graph is a normal probability plot of the blood thiocyanide concentration for the seven rats eating the raw 30% flaxseed diet. Statistical software reports the Shapiro-Wilk's normality
Bill lengths of a population of male blue jays have a normal distribution with mean 25.4 mm and standard deviation 0.8 mm. A bill is considered to be "short" if it is shorter than 24.0 mm. Suppose
Here is a list of life expectancies in 12 South American countries: 62,64,65,66,70,71,72,73,73,74,75,75 The mean of these data is 70, and the SD is 4.6. (You do not need to verify this.) Without
In a group of 18 patients, there were 8 men and 10 women. Suppose we were to choose two of them, at random and without replacement. What is the probability that they would be the same sex?
A researcher took a random sample of 20 mice and found that 5 of the 20 mice (25%) weighed more than 26 gm. In the context of this setting, explain what is meant by the sampling distribution of a
Tree diameters for a certain species of tree are nor-mally distributed with a mean of 20 cm and a standard deviation of 5 cm.(a) What is the probability that the diameter of a randomly chosen tree
Consider a hypothetical population of dogs in which there are four possible weights, all of which are equally likely: 40, 50, 65, or 70 pounds. A sample of size n = 2 is drawn from this population.
Researchers wanted to compare two drugs, for-moterol and salbutamol, in aerosol solution, for the treatment of patients who suffer from exercise-induced asthma. Patients were to take a drug, do some
Heights of American women ages 18-24 follow a normal distribution with an average of 64.3 inches. (Assume that measurements are made to the nearest 0.1 inch.) Moreover, 50% of the heights are between
A pharmacologist measured the concentration of dopamine in the brains of several rats. The mean concentration was 1,269 ng/gm and the standard deviation was 145 ng/gm.4 What was the standard error of
In evaluating a forage crop, it is important to measure the concentration of various constituents in the plant tissue. In a study of the reliability of such measurements, a batch of alfalfa was
A zoologist measured tail length in 86 individuals, all in the one-year age group, of the deermouse Peromyscus. The mean length was 60.43 mm and the standard deviation was 3.06 mm. The table presents
Refer to the mouse data of Exercise 6.2.4. Suppose the zoologist were to measure 500 additional animals from the same population. Based on the data in Exercise 6.2.4 (a) What would you predict would
In a report of a pharmacological study, the experimental animals were described as follows8: "Rats weighing 150 ± 10 gm were injected . . ." with a certain chemical, and then certain measurements
Levels of insoluble ash (gm/kg) were measured in a sample of small (0.3 gm) aliquots of dried and ground alfalfa.6 Below are three confidence intervals for the mean: One is a 95% confidence interval,

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