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Statistics For The Life Sciences 5th Edition Myra Samuels, Jeffrey Witmer, Andrew Schaffner - Solutions

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 superimposed. The fastest runner completed the 26.3-mile course in 2 hours and 9 minutes, or 129 minutes. The
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 are(a) 1,500 gm or less?(b) Between 1,325 and 1,500 gm?(c) 1,325 gm or more?(d) 1.475 gm or more?(e)
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 adult Swedish males follow approximately a normal distribution with mean 1,400 gm and standard
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 measured for each plot. These plot yields followed approximately a normal distribution with mean 88 lb
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 variety of wheat. The field was divided into many plots (each plot being 7 × 100 ft) and the yield
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 values (a) 164 or more? (b) 137 or less? (c) 186 or less? (d) 100 or more? (e) Between 159 and 186? (f)
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 determine intervals, centered at the mean, that include 68%, 95%, and 99.7% of the bill length in the
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 you know?
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 it is reasonable to believe that daily rainfall at Pismo Beach follows a normal distribution?
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 believe that the February 1 daily high temperatures in Juneau, Alaska, follow a normal distribution?
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 cycling race.(a) Consider the fastest riders. Are their times better than, worse than, or roughly equal
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 from a normal population? (b) The P-value for the Shapiro-Wilk test of normality for the data in
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 (approximately) as repeated independent observations from a normal distribution. Suppose the mean
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, the time intervals between "spike" discharges follow approximately a normal distribution with mean
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 can adequately be approximated by a normal curve, find the mean and standard deviation of the
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 deviation is 16 points. What percentage of children in the population have IQ scores (a) 140 or more? (b)
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 less and four will have scores higher than 80. Exercise 4.S.12 The intelligence quotient (IQ) score, as
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 concentration for that specimen and standard deviation equal to 4 U/l (see Example 2.2.12). Suppose that a
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 normal distribution, with a mean increase of 7.3 beats per minute and a standard deviation of 11.1. Let Y
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 15? Exercise 4.S.16 Resting heart rate was measured for a group of subjects; the subjects then drank 6
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 outlier on the upper end? Exercise 4.S.16 Resting heart rate was measured for a group of subjects; the
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 percentile of the bill length distribution.
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 consistent with this claim? (a) P-value = 0.0149 (b) P-value = 0.1345 (c) P-value = 0.0498 (d) P-value =
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 quantile plot goes with which histogram? How do you know? (There will be one normal quantile plot that is
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 less?(c) Between 120 and 150 cm?(d) Between 100 and 120 cm?(e) Between 150 and 180 cm?(f) 180 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 heights of a certain population of corn plants follow a normal distribution with mean 145 cm and
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 distribution with mean 145 cm and standard deviation 22 cm.
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 distribution with mean 145 cm and standard deviation 22 cm.
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 the value of z* such that 99% of the observations in the population are between - z* and + z* on the
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 Example 4.1.3). Let Y denote a randomly selected inter-spike interval. Find (a) Pr{Y > 15} (b) Pr{Y
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 $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 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 possible samples? (b) What is the sampling distribution of the total surgery costs for samples of size n
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 population, what is the sampling distribution of the total weight of the two dogs selected? That is, what are
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 diameter is 4.2 cm. and the standard deviation is 1.4 cm.4 Let represent the mean diameter of 25
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 situation, 65.68% of e fish are between 51 and 60 mm long. Suppose a random sample of four fish is
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 students took a random sample of size n and calculated the sample mean. Smith found that about 68%
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 concentration for that spec-men and standard deviation equal to 4 U/l (as in Exercise 4.S.15). Suppose a
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 distribution of the sample means from 100 samples, what kind of shape would we expect the histogram to
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 distribution of the sample means from 100 samples, what kind of shape would we expect the histogram to
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 Central Limit Theorem, would we expect the distribution of blood pressure readings to be less skewed
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 deviation of 9.6 If we take a sample of size n = 25. (a) what is the probability that the sample average
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 12- to 14-year-olds have serum cholesterol values between 145 and 165 mg/dl? (b) Suppose we were to
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 145 and 165? (b) What is the probability that the mean cholesterol value for the group will be
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 n young women from a certain population, and to use the sample mean y as an estimate of the
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 = 15 and the population mean is 2,600 ml. (c) How does Pr{E} depend on the population mean?
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 and 155 cm tall?(b) Suppose we were to choose at random from the population a large number of
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 the location (oh the Y-axis) of each peak. (b) Find the approximate area under each peak. (Hint: Use
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 peak.
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 appropriate approximate model for the distribution of over many such samples of size 50? That is, what
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 examined, and let P be the sample proportion of purple-flowered plants. It might happen, by chance, that P
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) of those sampled will have CMV. (a) Using the binomial distribution formula. (b) Using the normal
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 population. Find the probability that 85% or more of the sampled mussels will be infected, using 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 population of mussels (Mytilus edu-lis), 80% of the individuals are infected with an intestinal
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 approximation (a) Without the continuity correction. (b) With the continuity correction. Exercise 5.4.12 In a
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 approximation with the continuity correction.
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) Using the binomial distribution formula. (b) Using the normal approximation.
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 correction. Exercise 5.4.3 In the United States, 44% of the population has type O blood. Suppose a
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 contraceptive users () as an estimate of the population proportion (p). Suppose that in fact p = 0.12.
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. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15
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 Pr{E} for a sample of size n = 400.
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 be the event that is within ±0.05 of p. Use the normal approximation (without the continuity
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 the event that is within ±0.05 of p. Use the normal approximation (without the continuity
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 approximately a normal distribution with mean 88 lb and standard deviation 7 lb (as in Exercise 4.3.5). Let
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 is meant by the sampling distribution of the sample total.
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 population, and let μbe the population mean skull breadth. (a) Suppose μ = 50 mm. Find Pr{ is
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 average to his histogram of the sampling distribution of the mean. Suppose also that every day for 2
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, explain what is meant by the sampling distribution of the sample mean.
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 probability that he will be more than 72 inches tall. (b) If two men are chosen at random from 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 area Y of each plant. Assume that the population distribution of Y is approximately normal with mean
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 0.44? Use the normal approximation to the binomial with continuity correction.
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 (approximately) as repeated independent observations from a normal distribution (as in Exercise
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 population of mice, the weights at 20 days of age follow approximately a normal distribution with
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 1.1.(a) which of the following is a rough histogram for the data?(b) The median is___________the mean.
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 double-blind, who should be blinded and why?(a) An investigation of whether taking an aspirin every
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 either yellow or green. A certain cross between pea plants produces progeny that are in the ratio 3
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 inherently discrete or continuous? If categorical, is this variable nominal or ordinal?
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 days and then measured the amount of thiocyanate in the blood. Seven of the rats were randomly
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 14.6 mg/L.(a) How high must a blood thiocyanate concentration be in order to be in the top 15% 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 test P-value is 0.2675. (a) Would it be reasonable to regard the population from which these data
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 that a researcher has a large collection of these male blue jays and takes measurements each day on 10
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 doing any calculations, which data point had the largest contribution to the SD? That is, if we could
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 percentage.
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 will be between 16 cm and 23 cm?(b) Suppose we take a sample of n = 5 trees. What is the probability
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. We are interested in the sampling distribution of the total weight of the two dogs selected. How many
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 exercise, and then have their "forced expiratory volume" measured. There were 30 subjects
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 62.5 inches and 66.1 inches. What is the standard deviation of heights?
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 the mean if(a) 8 rats were measured?(b) 30 rats were measured?
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 dried, ground, and passed through a fine screen. Five small (0.3 gm) aliquots of the alfalfa were then
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 a frequency distribution of the data.7 Tail length (mm) Number of mice [52,54).......... 1 [54,56)
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 be the standard deviation of the 500 new measurements? (b) What would you predict would be the
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 were made on the rats. If the author intends to convey the degree of homogeneity of the group of
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, one is a 90% confidence interval, and the other is an 85% confidence interval. Without doing any

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