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biostatistics

Biostatistics For The Biological And Health Sciences 2nd Edition Marc Triola, Mario Triola, Jason Roy - Solutions

Physicians There are about 900,000 active physicians in the United States, and they have annual incomes with a distribution that is skewed instead of being normal. Many different samples of 40 physicians are randomly selected, and the mean annual income is computed for each sample.a. What is the
Good Sample? A geneticist is investigating the proportion of boys born in the world population. Because she is based in China, she obtains sample data from that country. Is the resulting sample proportion a good estimator of the population proportion of boys born worldwide?Why or why not?
Sampling Distribution Data Set 3 “Births” in Appendix B includes a sample of birth weights. If we explore this sample of 400 birth weights by constructing a histogram and finding the mean and standard deviation, do those results describe the sampling distribution of the mean? Why or why not?
Unbiased Estimators Data Set 3 “Births” in Appendix B includes birth weights of 400 babies. If we compute the values of sample statistics from that sample, which of the following statistics are unbiased estimators of the corresponding population parameters:sample mean; sample median; sample
Sampling with Replacement The Orangetown Medical Research Center randomly selects 100 births in the United States each day, and the proportion of boys is recorded for each sample.a. Do you think the births are randomly selected with replacement or without replacement?b. Give two reasons why
Births There are about 11,000 births each day in the United States, and the proportion of boys born in the United States is 0.512. Assume that each day, 100 births are randomly selected and the proportion of boys is recorded.a. What do you know about the mean of the sample proportions?b. What do
Significance For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that area. significantly high (or at least 2 standard deviations above the mean).b. significantly low (or at least 2 standard deviations below the
About % ¤ of the area is between z = -3.5 and z = 3.5 (or within 3.5 standard deviations of the mean). Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45–48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and
About % of the area is between z = -3 and z = 3 (or within 3 standard deviations of the mean). Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45–48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the
About % of the area is between z = -2 and z = 2 (or within 2 standard deviations of the mean). Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45–48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the
About % of the area is between z = -1 and z = 1 (or within 1 standard deviation of the mean). Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45–48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the
z0.15 Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.
z0.04 Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.
z0.02 Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.
z0.10 Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.
Find the bone density scores that can be used as cutoff values separating the lowest 3% and highest 3%.
If bone density scores in the bottom 2% and the top 2% are used as cutoff points for levels that are too low or too high, find the two readings that are cutoff values.
Find P10, the 10th percentile. This is the bone density score separating the bottom 10%from the top 90%.
Find P99, the 99th percentile. This is the bone density score separating the bottom 99%from the top 1%.
Less than 0.Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone
Greater than 0. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given
Greater than -3.75. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given
Less than 4.55. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given
Between -4.27 and 2.34. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the
Between -1.00 and 5.00. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the
Between -3.00 and 3.00. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the
Between -2.00 and 2.00. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the
Between -2.75 and –0.75. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of
Between and -2.55 and -2.00. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of
Between 1.50 and 2.50. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the
Between 2.00 and 3.00. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the
Greater than –3.05. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the
Greater than -2.00. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given
Greater than 0.18. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given
Greater than 0.25. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given
Less than 2.56. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given
Less than 1.28. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given
Less than -1.96. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given
Less than -1.23. Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given
Notation What does the notation za indicate?
Standard Normal Distribution Identify the two requirements necessary for a normal distribution to be a standard normal distribution.
Normal Distribution A normal distribution is informally described as a probability distribution that is “bell-shaped” when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.
Normal Distribution What’s wrong with the following statement? “Because the digits 0, 1, 2, . . . , 9 are the normal results from lottery drawings, such randomly selected numbers have a normal distribution.”
Using Probabilities for Identifying Significant Eventsa. Find the probability of getting exactly 1 sleepwalker among 5 adults.b. Find the probability of getting 1 or fewer sleepwalkers among 5 adults.c. Which probability is relevant for determining whether 1 is a significantly low number of
Using Probabilities for Identifying Significant Eventsa. Find the probability of getting exactly 4 sleepwalkers among 5 adults.b. Find the probability of getting 4 or more sleepwalkers among 5 adults.c. Which probability is relevant for determining whether 4 is a significantly high number of
Range Rule of Thumb for Significant Events Use the range rule of thumb to determine whether 3 is a significantly high number of sleepwalkers in a group of 5 adults.
Range Rule of Thumb for Significant Events Use the range rule of thumb to determine whether 4 is a significantly high number of sleepwalkers in a group of 5 adults.
Mean and Standard Deviation Find the mean and standard deviation for the numbers of sleepwalkers in groups of five.
Using Probabilities for Significant Eventsa. Find the probability of getting exactly 1 girl in 8 births.b. Find the probability of getting 1 or fewer girls in 8 births.c. Which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births: the result from part
Using Probabilities for Significant Eventsa. Find the probability of getting exactly 6 girls in 8 births.b. Find the probability of getting 6 or more girls in 8 births.c. Which probability is relevant for determining whether 6 is a significantly high number of girls in 8 births: the result from
Using Probabilities for Significant Eventsa. Find the probability of getting exactly 7 girls in 8 births.b. Find the probability of getting 7 or more girls in 8 births.c. Which probability is relevant for determining whether 7 is a significantly high number of girls in 10 births: the result from
Range Rule of Thumb for Significant Events Use the range rule of thumb to determine whether 6 girls in 8 births is a significantly high number of girls.
Range Rule of Thumb for Significant Events Use the range rule of thumb to determine whether 1 girl in 8 births is a significantly low number of girls.
Mean and Standard Deviation Find the mean and standard deviation for the numbers of girls in 8 births.
Diseased Seedlings An experiment involves groups of four seedlings grown under controlled conditions. The random variable x is the number of seedlings in a group that meet specific criteria for being classified as “diseased.”x P(x)0 0.805 1 0.113 2 0.057 3 0.009 4 0.002 Genetics. In Exercises
Genetic Disorder Three males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the three who inherit the X-linked genetic disorder.x P(x)0 0.4219 1 0.4219 2 0.1406 3 0.0156
Mortality Study For a group of four men, the probability distribution for the number x who live through the next year is as given in the accompanying table.x P(x)0 0.0000 1 0.0001 2 0.0006 3 0.0387 4 0.9606
Genetics Experiment A genetics experiment involves offspring peas in groups of four. A researcher reports that for one group, the number of peas with white flowers has a probability distribution as given in the accompanying table.x P(x)0 0.04 1 0.26 2 0.36 3 0.20 4 0.08
Male Color Blindness When conducting research on color blindness in males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness (based on data from the National Institutes of Health).x P(x)0
Genetic Disorder Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder.x P(x)0 0.031 1 0.156 2 0.313 3 0.313 4 0.156 5 0.031
a. Grades (A, B, C, D, F) earned in biostatistics classesb. Heights of students in biostatistics classesc. Numbers of students in biostatistics classesd. Eye colors of biostatistics studentse. Numbers of times biostatistics students must toss a coin before getting heads
a. Exact weights of the next 100 babies born in the United Statesb. Responses to the survey question “Which health plan do you have?”c. Numbers of families that must be surveyed before finding one with 10 childrend. Exact foot lengths of humanse. Shoe sizes (such as 8 or 8½) of humans
Significant For 100 births, P(exactly 56 girls) = 0.0390 and P(56 or more girls) = 0.136.Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question?
Probability Distribution For the accompanying table, is the sum of the values of P(x)equal to 1, as required for a probability distribution? Does the table describe a probability distribution?
Discrete or Continuous? Is the random variable given in the accompanying table discrete or continuous? Explain.
Random Variable The accompanying table lists probabilities for the corresponding numbers of girls in four births. What is the random variable, what are its possible values, and are its values numerical?
4.Diabetes Among adults in the United States, 11.5% have diabetes (based on data from the National Center for Health Statistics).a. Find the probability that a randomly selected adult does not have diabetes.b. Find the probability that two randomly selected adults both have diabetes.c. Find the
3.Government Health Plan Fox News broadcast a graph similar to the one shown here. The graph is intended to compare the number of people actually enrolled in a government health plan (left bar) and the goal for the number of enrollees (right bar). Does the graph depict the data correctly or is it
2.Analysis of Last Digits The accompanying table lists the last or rightmost digits of weights of the females listed in Data Set 1 “Body Data” in Appendix B. The last digits of a data set can sometimes be used to determine whether the data have been measured or simply reported. The presence of
1.Manatee Deaths Listed below are the annual numbers of manatee deaths from boats in Florida for each of the past 10 years, listed in chronological order.69 79 92 73 90 97 83 88 81 72a. Find the mean.b. Find the median.c. Find the range.d. Find the standard deviation.e. Find the variance.f.
Poisson: Deaths Currently, an average of 143 residents of Madison, CT (population 17,858), die each year (based on data from the U.S. National Center for Health Statistics).a. Find the mean number of deaths per day.b. Find the probability that on a given day, there are no deaths.c. Find the
7.Condom Failure Rate According to the Department of Health and Human Services, the failure rate for male condoms is 18%. The accompanying table is based on the failure rate of 18%, where x represents the number of condoms that fail when six are tested.a. Does the table describe a probability
6.Security Survey In a USA Today poll, subjects were asked if passwords should be replaced with biometric security, such as fingerprints. The results from that poll have been used to create the accompanying table. Does this table describe a probability distribution? Why or why not?
5.Cholesterol If the group of five adults includes exactly 1 with high cholesterol, is that value of 1 significantly low?
4.Cholesterol If all five of the adults have high cholesterol, is five significantly high? Why or why not?
3.Cholesterol Find the mean and standard deviation for the numbers of adults in groups of five who have high cholesterol.
2.Cholesterol Find the probability that at least one of the five adults has high cholesterol.Does the result apply to five adults from the same family? Why or why not?
1.Cholesterol Find the probability that exactly two of the five adults have high cholesterol.
Drinking What is the probability that fewer than three of the five adult males are heavy drinkers? If we were to find that among 5 randomly selected adult males, there are 4 heavy drinkers, is 4 significantly high?
9.Drinking What does the probability of 0+ indicate? Does it indicate that among five randomly selected adult males, it is impossible for all of them to be heavy drinkers?
8.Drinking Based on the table, the standard deviation is 0.5 male. What is the variance? Include appropriate units.
7.Drinking Find the mean of the number of heavy drinkers in groups of five randomly selected adult males.
6.Drinking Does the table describe a probability distribution? Why or why not?
5.Smoking Find the probability that the first 8 randomly selected males include exactly 3 who smoke.
4.Smoking For a random sample of 64 males, find the numbers separating the outcomes that are significantly high or significantly low.
3.Smoking Are the results from Exercises 1 and 2 statistics or parameters?
1.Smoking Find the mean number of smokers in groups of 64 randomly selected adult males.
17. Probability Histogram for a Poisson Distribution Construct the probability histogram for Exercise 16. Is the Poisson probability distribution a normal distribution or is it skewed?
Diphtheria During the past 34 years, there were 56 cases of diphtheria in the United States.a. Find the mean number of cases of diphtheria per year. Express the result with five decimal places.b. Find the probability of no cases of diphtheria in a year.c. Find the probability that the number of
2.Smoking Find the standard deviation of the number of smokers in groups of 64 randomly selected adult males.
Rubella During the last 13 years in the United States, there were 138 cases of rubella.a. Find the mean number of cases of rubella per year. Round the result to four decimal places.b. Find the probability of no cases of rubella in a year.c. Find the probability of exactly 9 cases of rubella in a
Dandelions Dandelions are studied for their effects on crop production and lawn growth.In one region, the mean number of dandelions per square meter was found to be 7.0 (based on data from Manitoba Agriculture and Food).a. Find the probability of no dandelions in an area of 1 m2.b. Find the
Car Fatalities The recent rate of car fatalities was 33,561 fatalities for 2969 billion miles traveled (based on data from the National Highway Traffic Safety Administration). Find the probability that for the next billion miles traveled, there will be at least one fatality. What does the result
Disease Cluster Neuroblastoma, a rare form of cancer, occurs in 11 children in a million, so its probability is 0.000011. Four cases of neuroblastoma occurred in Oak Park, Illinois, which had 12,429 children.a. Assuming that neuroblastoma occurs as usual, find the mean number of cases in groups of
World War II Bombs In analyzing hits by V-1 buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions.a. Find the probability that a randomly selected region had exactly 2 hits.b. Among the 576
Deaths from Horse Kicks A classical example of the Poisson distribution involves the number of deaths caused by horse kicks to men in the Prussian Army between 1875 and 1894.Data for 14 corps were combined for the 20-year period, and the 280 corps-years included a total of 196 deaths. After finding
9.Murders In a recent year, there were 333 murders in New York City. Find the mean number of murders per day; then use that result to find the probability that in a day, there are no murders.Does it appear that there are expected to be many days with no murders?
8.Births Find the probability that in a day, there will be at least 2 births. Births. In Exercises 5–8, assume that the Poisson distribution applies, assume that the mean number of births at the NYU Langone Medical Center is 11.5863 per day, and proceed to find the probability that in a randomly
7.Births Find the probability that in a day, there will be at least 1 birth. Births. In Exercises 5–8, assume that the Poisson distribution applies, assume that the mean number of births at the NYU Langone Medical Center is 11.5863 per day, and proceed to find the probability that in a randomly
6.Births Find the probability that in a day, there will be exactly 9 births. Births. In Exercises 5–8, assume that the Poisson distribution applies, assume that the mean number of births at the NYU Langone Medical Center is 11.5863 per day, and proceed to find the probability that in a randomly

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