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biostatistics

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

5.Births Find the probability that in a day, there will be exactly 12 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
4.Probability if 0 For Formula 5-9, what does P(0) represent? Simplify Formula 5-9 for the case in which x = 0.
3.Poisson Probability Distribution The random variable x represents the number of patient admissions in a day, as described in Exercise 1. Assume that the random variable x has a Poisson distribution. What are the possible values of x? Is a value of x = 90.3 possible? Is x a discrete random
2.Patient Admissions Use the same patient admission data given in Exercise 1. Let the random variable x represent the number of patient admissions in one day, and assume that it has a Poisson distribution. What is the standard deviation for the values of the random variable x?What is the variance?
1.Notation In analyzing patient admissions at NYU Langone Medical Center, we find that 31,645 patients were admitted in a recent year (based on data from the NYU Langone website).Assume that we want to find the probability of exactly 85 patient admissions in a randomly selected day. In applying
Geometric Distribution If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P1x2 = p11 - p2 x-1, where p is the
Vaccine For a specific group of subjects, there is a 5% chance of influenza (“flu”). When 80 subjects were treated with a vaccine, only one of them presented with influenza.a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are
Hybrids One of Mendel’s famous experiments with peas included 47 offspring, and 34 of them had long stems. Mendel claimed that under the same conditions, 75% of offspring peas would have long stems. Assume that Mendel’s claim of 75% is true, and assume that a sample consists of 47 offspring
Clinical Trial A treatment for hypertension has been found to be successful in 60% of the patient population. In a test of a new treatment, 40 subjects are treated for hypertension and 29 of these subjects experience success with the new treatment.a. Assuming that the old success rate of 60% still
Gender Selection At an early stage of clinical trials of the XSORT method of gender selection, 14 couples using that method gave birth to 13 girls and 1 boy.a. Assuming that the XSORT method has no effect and boys and girls are equally likely, use the range rule of thumb to identify the limits
AAA Batteries AAA batteries are made by companies including Duracell, Energizer, Eveready, and Panasonic, and they are used to power Prestige Medical Xenon pocket otoscopes(those things that physicians use to look in your ears). When purchasing bulk orders of AAA batteries, a manufacturer of
Aspirin The MedAssist Pharmaceutical Company receives large shipments of aspirin tablets and uses this acceptance sampling plan: Randomly select and test 40 tablets, and then accept the whole batch if there is only one or none that doesn’t meet the required specifications.If one shipment of 5000
Blood Donor Testing The American Red Cross tests every unit of donated blood for several infectious diseases, including hepatitis B, hepatitis C, HIV, syphilis, and West Nile virus infection. Blood samples from 16 donors are combined and tested, and all 16 individual samples are approved only if
HIV It is estimated that worldwide, 1% of those aged 15–49 are infected with the human immunodeficiency virus (HIV) (based on data from the National Institutes of Health). In tests for HIV, blood samples from 36 people are combined. What is the probability that the combined sample tests positive
Hybrids Assume that offspring peas are randomly selected in groups of 16.a. Find the mean and standard deviation for the numbers of peas with green pods in the groups of 16.b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.c. Is a
Hybrids Assume that offspring peas are randomly selected in groups of 10.a. Find the mean and standard deviation for the numbers of peas with green pods in the groups of 10.b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.c. Is
Gender Selection Assume that the groups consist of 16 couples.a. Find the mean and standard deviation for the numbers of girls in groups of 16 births.b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.c. Is the result of 11 girls a
Gender Selection Assume that the groups consist of 36 couples.a. Find the mean and standard deviation for the numbers of girls in groups of 36 births.b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.c. Is the result of 26 girls a
If 12 adults are randomly selected, find the probability that fewer than 3 of them do not require vision correction.
If 10 adults are randomly selected, find the probability that at least 3 of them do not require vision correction.
If 20 adults are randomly selected, find the probability that exactly 5 of them do not require vision correction.
If 8 adults are randomly selected, find the probability that exactly 2 of them do not require vision correction.
Find the probability that at least one answer is correct. MCAT Test. In Exercises 15–20, assume that random guesses are made for eight multiple choice questions on an MCAT test, so that there are n 8 trials, each with probability of success (correct) given by p 0.20. Find the indicated
Find the probability of no correct answers. MCAT Test. In Exercises 15–20, assume that random guesses are made for eight multiple choice questions on an MCAT test, so that there are n 8 trials, each with probability of success (correct) given by p 0.20. Find the indicated probability for the
Find the probability that the number x of correct answers is no more than 2. MCAT Test. In Exercises 15–20, assume that random guesses are made for eight multiple choice questions on an MCAT test, so that there are n 8 trials, each with probability of success (correct) given by p 0.20. Find
Find the probability that the number x of correct answers is fewer than 3. MCAT Test. In Exercises 15–20, assume that random guesses are made for eight multiple choice questions on an MCAT test, so that there are n 8 trials, each with probability of success (correct) given by p 0.20. Find the
Find the probability that the number x of correct answers is at least 4. MCAT Test. In Exercises 15–20, assume that random guesses are made for eight multiple choice questions on an MCAT test, so that there are n 8 trials, each with probability of success (correct) given by p 0.20. Find the
Find the probability that the number x of correct answers is exactly 7. MCAT Test. In Exercises 15–20, assume that random guesses are made for eight multiple choice questions on an MCAT test, so that there are n 8 trials, each with probability of success (correct) given by p 0.20. Find the
Vision Correction 53% of adults use eyeglasses for vision correction (based on data from a Vision Council survey). Four adults are randomly selected.a. Use the multiplication rule to find the probability that the first three use eyeglasses and the fourth does not use eyeglasses. That is, find
Guessing Answers Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT) typically use multiple choice questions, each with five possible answers(a,b, c,d, e), one of which is correct. Assume that you guess the answers to the first three questions.a. Use the multiplication
Defibrillators Counting the numbers of defects in each of 500 defibrillators.
Defibrillators Determining whether each of 500 defibrillators is acceptable or defective.
Nicorette Treating 50 smokers with Nicorette and recording whether there is a “yes” response when they are asked if they experience any mouth or throat soreness.
Nicorette Treating 50 smokers with Nicorette and asking them how their mouth and throat feel.
8.Clinical Trial of Lipitor Treating 863 subjects with Lipitor (atorvastatin) and asking each subject how their head feels (based on data from Pfizer, Inc.).
7.Clinical Trial of Lipitor Treating 863 subjects with Lipitor (atorvastatin) and recording whether there is a “yes” response when they are each asked if they experienced a headache(based on data from Pfizer, Inc.).
Clinical Trial of YSORT The YSORT method of gender selection, developed by the Genetics & IVF Institute, was designed to increase the likelihood that a baby will be a boy.When 291 couples use the YSORT method and give birth to 291 babies, the genders of the babies are recorded.
Clinical Trial of YSORT The YSORT method of gender selection, developed by the Genetics & IVF Institute, was designed to increase the likelihood that a baby will be a boy.When 291 couples used the YSORT method and gave birth to 291 babies, the weights of the babies were recorded.
Notation of 0 Using the same survey from Exercise 3, the probability of randomly selecting 30 of the 1020 adults and getting exactly 24 who wash hands after using public transportation is represented as 0+. What does 0+ indicate? Does 0+ indicate that it is impossible to get exactly 24 adults who
Independent Events Based on a KRC Research survey, when 1020 adults were asked about hand hygiene, 44% said that they wash their hands after using public transportation. Consider the probability that among 30 different adults randomly selected from the 1020 who were surveyed, there are at least 10
2.Variation and Notation Assume that we want to find the probability that among five offspring peas, exactly two of them have green pods. Also assume that 75% of offspring peas have green pods (and the others have yellow pods).a. Identify the values of n, x, p, and q.b. For groups of 5 randomly
Hybridization Assume that 75% of offspring peas have green pods. Suppose we want to find the probability that when five offspring peas are randomly selected, exactly two of them are green. What is wrong with using the multiplication rule to find the probability of getting two peas with green pods
Blood Pressure and Platelets Given below are the systolic blood pressure measurements(mm Hg) and blood platelet counts (1000 cells>mL) of the first few subjects included in Data Set 1 “Body Data” in Appendix B. Construct a graph suitable for exploring an association between systolic blood
Sampling Eye Color Based on a study by Dr. P. Sorita Soni, eye colors in the United States are as follows: 40% brown, 35% blue, 12% green, 7% gray, 6% hazel.a. A statistics instructor collects eye color data from her students. What is the name for this type of sample?b. Identify one factor that
Organ Donors USA Today provided information about a survey (conducted for Donate Life America) of 5100 adult Internet users. Of the respondents, 2346 said they are willing to donate organs after death. In this survey, 100 adults were surveyed in each state and the District of Columbia, and results
Fatal Drunk Driving Use the same data given in Exercise 1.a. Identify the 5-number summary and also identify any values that appear to be outliers.b. Construct a boxplot.c. Construct a stemplot.
Fatal Drunk Driving Listed below are the blood alcohol concentrations (g>dL) of drivers convicted of drunk driving in fatal car crashes (based on data from the National Highway Traffic Safety Administration).0.09 0.11 0.11 0.13 0.14 0.15 0.17 0.17 0.18 0.18 0.23 0.35 Find the value of the following
Redundancy Using battery-powered alarm clocks, it is estimated that the probability of failure on any given day is 1>1000.a. What is the probability that the alarm clock works for an important event?b. When using two alarm clocks for an important event, what is the probability that at least one of
Composite Sampling for Diabetes Currently, the rate for new cases of diabetes in a year is 3.4 per 1000 (based on data from the Centers for Disease Control and Prevention). When testing for the presence of diabetes, the Portland Diagnostics Laboratory saves money by combining blood samples for
National Statistics Daya. If a person is randomly selected, find the probability that his or her birthday is October 18, which is National Statistics Day in Japan. Ignore leap years.b. If a person is randomly selected, find the probability that his or her birthday is in October.Ignore leap years.c.
Vision Correction About 75% of the U.S. population uses some type of vision correction(such as glasses or contact lenses).a. If someone is randomly selected, what is the probability that he or she does not use vision correction?b. If four different people are randomly selected, what is the
All Three Successful If 3 patients are randomly selected without replacement, find the probability that all three had successful treatments.
Complement If A represents the event of randomly selecting one patient included in the table and getting someone who had a successful treatment, what does A represent? Find the value of P1A2.
Complement If A represents the event of randomly selecting one patient included in the table and getting someone who was treated with surgery, what does A represent? Find the value of P1A2.
Both Successful If 2 patients are randomly selected with replacement, find the probability that they both had successful treatments.
Both Successful If 2 patients are randomly selected without replacement, find the probability that they both had successful treatments.
No Success or Splint If 1 of the patients is randomly selected, find the probability of getting someone who had an unsuccessful treatment or was treated with a splint.
Success or Surgery If 1 of the patients is randomly selected, find the probability of getting a patient who had a successful treatment or was treated with surgery.
Success Find the probability of randomly selecting a patient and getting one with a successful treatment, given that the patient was treated with surgery.
Success Find the probability of randomly selecting a patient and getting one with a successful treatment, given that the patient was treated with splinting.
Success If 1 of the patients is randomly selected, find the probability of selecting someone with a successful treatment.
Find the probability of randomly selecting 1 of the subjects and getting 1 who developed flu, given that the subject was given the vaccine treatment.
9.Find the probability of randomly selecting 2 subjects without replacement and finding that they both developed flu.
8.If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 who had the vaccine treatment and developed flu.
7.If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 who had the vaccine treatment or developed flu.
6.If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 that developed flu.
5.Subjective Probability Estimate the probability that the next time you get a cut, it requires stitches.
Sigmoidoscopy , Colonoscopy Based on data from the Centers for Disease Control, 67.7% of males over the age of 50 have had a sigmoidoscopy or colonoscopy. If two males over the age of 60 are randomly selected, what is the probability that they both have had a sigmoidoscopy or colonoscopy?
3.Months If a month is randomly selected after mixing the pages from a calendar, what is the probability that it is a month containing the letter y?
2.Likelihood of Disease After obtaining a patient’s positive test result, a physician concludes that there is a 30% chance that the subject has a disease. What is the probability that the subject does not have the disease?
1.Standard Tests Standard tests, such as the MCAT, tend to make extensive use of multiplechoice questions because they are easy to grade using software. If one such multiple-choice question has possible correct answers ofa, b,c, d,e, what is the probability of a wrong answer if the answer is a
Handshakesa. Five physicians gather for a meeting about a patient. If each physician shakes hands with each other physician exactly once, what is the total number of handshakes?b. If n physicians shake hands with each other exactly once, what is the total number of handshakes?c. How many different
Computer Variable Names A common computer programming rule is that names of variables must be between one and eight characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example, allowable variable
Mendel’s Peas Mendel conducted some his famous experiments with peas that were either smooth yellow plants or wrinkly green plants. If four peas are randomly selected from a batch consisting of four smooth yellow plants and four wrinkly green plants, find the probability that the four selected
Morse Codes The International Morse code is a way of transmitting coded text by using sequences of on>off tones. Each character is 1 or 2 or 3 or 4 or 5 segments long, and each segment is either a dot or a dash. For example, the letter G is transmitted as two dashes followed by a dot, as in — —
Designing Experiment Clinical trials of Nasonex involved a group given placebos and another group given treatments of Nasonex. Assume that a preliminary Phase I trial is to be conducted with 12 subjects, including 6 men and 6 women. If 6 of the 12 subjects are randomly selected for the treatment
Lightning and Lottery As of this writing, the Mega Millions lottery is run in 44 states.Winning the jackpot requires that you select the correct five different numbers between 1 and 75 and, in a separate drawing, you must also select the correct single number between 1 and 15.Find the probability
Phase I of a Clinical Trial A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a Phase I test of bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with
What a Word! One of the longest words in standard statistics terminology is “homoscedasticity.”How many ways can the letters in that word be arranged?
Identity Theft with Credit Cards Credit card numbers typically have 16 digits, but not all of them are random.a. What is the probability of randomly generating 16 digits and getting your MasterCard number?b. Receipts often show the last four digits of a credit card number. If only those last four
Amino Acids With 8 different amino acids available, 5 are to be selected to form a chain(called a polypeptide chain) in which order counts. How many different chains are possible?
Card Access You have an identification card used for access to a secure area of the Wellington Medical Center. It’s dark and you can’t see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters
Corporate Officers and Committees The Newport Medical Supply Company must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a strategic planning committee with four different members. There are 10 qualified
Classic Counting Problem A classic counting problem is to determine the number of different ways that the letters of “Mississippi” can be arranged. Find that number.
Phone Numbers Current rules for telephone area codes allow the use of digits 2–9 for the first digit and 0–9 for the second and third digits. How many different area codes are possible with these rules? That same rule applies to the exchange numbers, which are the three digits immediately
FedEx Deliveries With a short time remaining in the day, a FedEx driver has time to make deliveries at 6 locations among the 9 locations remaining. How many different routes are possible?
ZIP Code If you randomly select five digits, each between 0 and 9, with repetition allowed, what is the probability you will get the ZIP code of the Secretary of Health and Human Services?
Emergency Room Instead of treating emergency room patients in the order that they arrive, it is common to treat those with more serious problems first. If an emergency room has seven different patients, how many ways can they be arranged in sequence?
Clinical Trial In a clinical trial of the drug atorvastatin (Lipitor), one group of subjects was given placebos, a second group was given treatments of 10 mg, a third group was given treatments of 20 mg, a fourth group was given treatments of 40 mg, and a fifth group was given treatments of 80 mg.
Electricity The control panel for an MRI device uses five color-coded wires. If we troubleshoot by testing two wires at a time, how many different tests are required for every possible pairing of two wires?
Safety with Numbers A safe “combination” consists of four numbers between 0 and 99, and the safe is designed so that numbers can be repeated. If someone tries to gain access to the safe, what is the probability that he or she will get the correct combination on the first attempt?Assume that the
Survey Reliability A health survey with 12 questions is designed so that 3 of the questions are identical and 4 other questions are identical (except for minor changes in wording).How many different ways can the 12 questions be arranged?
Scheduling Routes A new director of the Veterans Health Administration plans to visit one hospital in each of five different states. If the five states are randomly selected from all 50 states without replacement and the order is also random, what is the probability that she visits Idaho, Oregon,
Radio Station Call Letters If radio station call letters must begin with either K or W and must contain a total of either three or four letters, how many different possibilities are there?
9.Blood Test Quest Diagnostics has just received 8 different blood samples. If they are tested in random order, what is the probability that they are tested in the alphabetical order of the subjects who provided the samples?
8.Review Board The supervisor at the Wellington Medical Center must select three nurses from 11 who are available for a review board. How many different ways can that be done?
7.Assigning Shifts The staff supervisor at the Wellington Medical Center must assign a team of two physicians to work the emergency room on Saturday night. If there are 19 physicians available and two of them are randomly selected, what is the probability of getting the two youngest physicians?
6.Social Security Numbers A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security
In Exercises 5–30, express all probabilities as fractions.5.Pin Numbers The Kinsale Medical Supply Company issues pin numbers to its employees so that they can access an online database. A hacker must randomly guess the correct pin code for the Information Technology supervisor, and that pin
4.Notation Evaluate 9P4. What does the result represent?

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