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mathematics
mathematical applications for the management

Mathematical Applications For The Management, Life And Social Sciences 12th Edition Ronald J. Harshbarger, James J. Reynolds - Solutions

For the binomial experiments in Problem, find the normal approximation of the probability of fewer than 22 successes in 87 trials if p = 0.2.
If a group of 30 women use diaphragms correctly and consistently, how many of these 30 women could be expected to become pregnant in a year?The table gives the percent of women who become pregnant during 1 year of use with different types of contraceptives. The “Typical Use” column includes
For the binomial experiments in Problem, find the normal approximation of the probability of fewer than 70 successes in 180 trials if p = 0.4.
For the binomial experiments in Problem, find the normal approximation of the probability of at least 423 successes in 6000 trials if p = 0.07.
The Pennsylvania Daily Number is a three-digit number game that costs $1 per “number” and has a winning ticket payoff of $500. On April 24, 1980, the winning number was 666. Several weeks later it was discovered that the April 24 drawing had been fixed. Exposure of the scandal revealed that all
Suppose that 2% of the computer chips shipped to an assembly plant are defective.(a) What is the probability that 10 of 100 chips chosen from the shipment will be defective?(b) What is the expected number of defective chips in the shipment if it contains 1500 chips?
In Problem, find the mean, variance, and standard deviation for each probability distribution.Pr(x) = x/10; x = 2, 3, 5
The table summarizes the number of mobile phones per 100 people in the population of each of the 64 countries with the largest number of phones.(a) Use class marks and the number of countries (frequency) to find the mean number of mobile phones per 100 people in the population for these
The probability that a certain couple will have a blue-eyed child is 1/4, and they have 4 children. What is the probability that(a) 1 of their children has blue eyes?(b) 2 of their children have blue eyes?(c) At least 1 of their children has blue eyes?
A fire detection device uses 4 temperature sensors that work independently so that any one of them can activate an alarm. If the temperature reaches 200oF, each sensor has probability 0.8 of activating the alarm.(a) Find the probability that the alarm is not activated when the temperature reaches
A hospital buys blood pressure monitors in lots of 1000. On average, 1 out of 1000 is defective. If 10 are selected from one lot, what is the probability that none is defective?
For the binomial experiments in Problem, find the normal approximation of the probability of at least 95 successes in 500 trials if p = 0.2.
In Problem, find the mean, variance, and standard deviation for each probability distribution.Pr(x) = x/21; x = 0, 1, 2, 3, 4, 5, 6
The probability that a sharpshooter will hit a target each time he shoots is 0.98. What is the probability that he will hit the target 10 times in 10 independent shots?
For the following probability distribution, find the expected value E(x).x Pr(x)1 ............ 0.22 ............ 0.33 ............ 0.44 ............ 0.1
The table gives the projected 2020 population of the United States.(a) Use the class marks and the given number (frequency) in each class to find the mean age.(b) In third world countries where the birth rate is higher and the life span is shorter, which group—under 30, 30–59, or 60 and
For the binomial experiments in Problem, find the normal approximation of the probability of no more than 450 successes in 1000 trials if p = 0.4.
Find the probability that a z-score from the standard normal distribution will lie within each of the intervals in Problem.z > -1.6
The table gives the ages of a sample of householders in primary families. Use this table in Problem.Age of Householder (years) Number (thousands)15–24 ............................................................... 339525–34
For the binomial experiments in Problem, find the normal approximation of the probability of no more than 80 successes in 100 trials if p = 0.7.
Find the probability that a z-score from the standard normal distribution will lie within each of the intervals in Problem.z < 1.2
The table gives the ages of a sample of householders in primary families. Use this table in Problem.Age of Householder (years) Number (thousands)15–24 ............................................................... 339525–34
For the binomial experiments in Problem, find the normal approximation of the probability of more than 120 successes in 200 trials if p = 0.6.
Find the probability that a z-score from the standard normal distribution will lie within each of the intervals in Problem.z > 1.5
Use a normal approximation to a binomial distribution to find the probability that x ≤ 25 if n = 120 and p = 0.2.
For the binomial experiments in Problem, find the normal approximation of the probability of more than 80 successes in 100 trials if p = 0.7.
Find the probability that a z-score from the standard normal distribution will lie within each of the intervals in Problem.z > 2
In Problems, five balls are drawn with replacement from a bag containing 6 red balls and 4 black balls. Find the probability that(a) All 5 balls will be red.(b) 4 of the balls will be black.(c) At least 2 red balls will be drawn.
Use a normal approximation to a binomial distribution to find the probability that x ≥ 10 if n = 50 and p = 0.3.
For the binomial experiments in Problem, find the normal approximation of the probability of between 65 and 70 successes (inclusive) in 120 trials if p = 0.5.
Find the probability that a z-score from the standard normal distribution will lie within each of the intervals in Problem.1.85 ≤ z ≤ 2.85
The random variable x has a normal distribution with mean 22 and standard deviation 8. Find B so that Pr(x > B) = 0.02.
For the binomial experiments in Problem, find the normal approximation of the probability of between 75 and 80 successes (inclusive) in 150 trials if p = 0.6.
In Problems, five balls are drawn with replacement from a bag containing 6 red balls and 4 black balls. Find the probability that(a) 2 of the balls will be red.(b) All 5 balls will be black.(c) At least 3 of the balls will be black.
When a pair of dice is rolled, a sum of 5 occurs with probability 1/9. If these dice are rolled 13 times, find the probability that a sum of 5(a) Occurs exactly 6 times.(b) Does not occur.(c) Occurs at least once.
For the normal distribution with mean 70 and standard deviation 12, find:(a) Pr(73 ≤ x ≤ 97)(b) Pr(65 ≤ x ≤ 84)(c) Pr(x > 84)
For the binomial experiments in Problem, find the normal approximation of the probability of 17 successes in 87 trials if p = 0.2.
Find the probability that a z-score from the standard normal distribution will lie within each of the intervals in Problem.-2.45 ≤ z ≤ -1.45
A fair die is rolled 12 times. What is the probability that an “ace” (a 1) will occur(a) On anyone roll?(b) 5 times in 12 rolls? (c) On none of the 12 rolls?
If the variable x is normally distributed, with a mean of 16 and a standard deviation of 6, find the following probabilities.(a) Pr(14 ≤ x ≤ 22)(b) Pr(x ≤ 22)(c) Pr(22 ≤ x ≤ 24)
For the binomial experiments in Problem, find the normal approximation of the probability of 96 successes in 180 trials if p = 0.4.
Find the probability that a z-score from the standard normal distribution will lie within each of the intervals in Problem.-1.9 ≤ z ≤ -1.1
If a fair die is rolled 3 times, what is the probability that(a) A 5 will result 2 times out of the 3 rolls?(b) An odd number will result 2 times?(c) A number divisible by 3 will occur 3 times?(d) At least one 5 will occur?
For the sample data in the table, find the mean, median, and mode.Score Frequency20 ...................... 521 ...................... 722 ...................... 323 ...................... 424 ...................... 2
Find the probability that a z-score from the standard normal distribution will lie within each of the intervals in Problem.-1.25 ≤ z ≤ 3
Suppose a fair coin is tossed 6 times. What is the probability of(a) 6 heads?(b) 3 heads?(c) 2 heads?(d) At least 2 heads?
Use the data in the frequency table in Problems.Score Frequency1 ............................. 42 ............................. 63 ............................. 84 ............................. 35 ............................. 5What is the median of the
Use the data in the frequency table in Problems.Score Frequency1 ............................. 42 ............................. 63 ............................. 84 ............................. 35 ............................. 5What is the mean of the data?
Use the data in the frequency table in Problems.Score Frequency1 ............................. 42 ............................. 63 ............................. 84 ............................. 35 ............................. 5What is the mode of the data?
For the probability distribution shown, find the mean, variance, and standard deviation. X 10 12 15 18 20 25 Pr(x) 0.1 0.3 0.1 0.2 0.1 0.2
If the probability of success on each of 8 independent trials of an experiment is 0.4, what is the probability of(a) 5 successes?(b) At most 7 successes?
Use the data in the frequency table in Problems.Score Frequency1 ............................. 42 ............................. 63 ............................. 84 ............................. 35 ............................. 5Construct a frequency
If the probability of success on each of 6 independent trials of an experiment is 0.3, what is the probability of(a) 4 successes? (b) At least 1 success?
Find the expected value of the variable x for the probability distribution given in the table. 3 4 5 6 7 8 Pr(x) 0.2 0.3 0.1 0.1 0.2 0.1
If x is a random variable, what properties must Pr(x) satisfy to be a discrete probability distribution function?
Suppose the coin in Problem 1 is tossed 12 times.(a) What is the expected number of heads?(b) Find the mean, variance, and standard deviation of the distribution of heads.
If the probability of success on each trial of an experiment is 0.4, what is the probability of 5 successes in 7 trials?
If a coin is “loaded” so that the probability that a head will occur on each toss is 1/3, what is the probability that(a) 3 heads will result from 5 tosses of the coin?(b) At least 3 heads will occur in 5 tosses of the coin?
Find the probability that a z-score from the standard normal distribution will lie within each of the intervals in Problem.2.1 ≤ z ≤ 3.0
In an actual case,* probability was used to convict a couple of mugging an elderly woman. Shortly after the mugging, a young White woman with blonde hair worn in a ponytail was seen running from the scene of the crime and entering a yellow car that was driven by a Black man with a beard. A couple
A bag contains three white balls numbered 1, 2, 3 and four black balls numbered 4, 5, 6, 7. If one ball is drawn at random, find the probability of each event described in Problems.(a) The ball is red.(b) The ball is numbered less than 8.
A bag contains three white balls numbered 1, 2, 3 and four black balls numbered 4, 5, 6, 7. Two balls are drawn without replacement. Find the probability of each event described in Problems.Both balls are odd-numbered.
A bag contains 4 white, 7 black, and 6 green balls. What is the probability that a ball drawn at random from the bag is white or green?
In Problems, find the steady-state vector associated with the given transition matrix from Problems 9–12. 0.5 0.3 0.2 C = 0.3 0.5 0.2 0.1 0.1 0.8
According to the American Cancer Society, 199 of 200 mammograms turn out to be normal. What is the probability that the mammogram of a woman chosen at random will show an abnormality?
Would the probabilities for which car he drives 100 days from now depend on whether he drove a Ford or an Audi today?Use the following information for Problems. A man owns an Audi, a Ford, and a VW. He drives every day and never drives the same car two days in a row. These are the probabilities
The table gives the numbers of new HIV infections in various categories for the United States and six dependent areas in 2014. Use the table to find the probability that a person diagnosed in 2014 was:(a) Female.(b) Female and an injected drug user.(c) Male or heterosexual. Total Heterosexual
Human blood is classified by blood type, which indicates the presence or absence of the antigens A, B, and Rh, as follows.A present Type AB present Type BBoth A and B present Type ABNeither A nor B present Type OEach of these types is combined with a + or - sign to indicate whether the Rh antigen
In 2014, the death rate from motor vehicle accidents was 10.7 per 100,000 people and the death rate from falls was 9.6 per 100,000 people. What is the probability that a death in 2014 was from a motor vehicle accident or from a fall?
A certain make of car comes with either an automatic or manual transmission and in one of three styles: convertible, sedan, or SUV. The following table shows the probability of each possible style and transmission.(a) Find the probability that a car is an automatic.(b) Find the probability that a
Construct an equiprobable sample space that gives the possible combinations of male and female children in a family with three children.
Meow Chow offers a free coin in each bag of cat food. If each 10,000-bag shipment has one gold coin, 2 silver dollars, 5 quarters, 20 dimes, 50 nickels, and 9922 pennies, what is the probability that a bag of Meow Chow cat food selected at random will have a penny in it?
A regional medical center plans to evaluate its administrative personnel and procedures. Ten of the center’s 80 nurses will be chosen to complete an in-depth evaluation.(a) In how many ways can the 10 nurses be chosen?(b) If 52 of the nurses are women, in how many ways can the 10 nurses consist
If the probability of rain today is 30%, what are the odds against rain today?
The odds that a celebrity marriage will last a lifetime are 3 to 1. What is the probability that a celebrity marriage chosen at random will last a lifetime?
Assuming that there are 365 different birthdays, find the probability that of 20 people chosen randomly,(a) No two will have the same birthday.(b) At least two will have the same birthday.
If a baseball player has 1150 at-bats and 320 hits, what is the probability that he will get a hit his next time at bat?
On average, 6 articles out of each 250 produced by a certain machine are defective. What is the probability that an article chosen at random is defective?
In taking a quiz with 6 multiple-choice questions, a student knows that two of the possible five answers to the first question are not correct. What is the probability of her getting the correct answer to the first question?
A quiz consists of 8 matching questions with 8 possible matches from which to choose. If a student guesses on the first question, what is the probability that he will get the correct answer?
The best Major League shortstops make a fielding error on about 2.5% of their plays. If each fielding attempt is independent, find the probability of(a) No errors in 8 plays (a typical game).(b) At least one error in 35 plays.
What is the probability that a randomly selected couple with two children has(a) One child of each sex?(b) Two children of the same sex?
Ronald Lee has been told by a company that the probability that he will be offered a job in the quality control department is 0.6 and the probability that he will be asked to supervise the department if he is offered the job is 0.1. What is the probability that he will be offered the job and asked
An auto dealer has 4 cars, 2 trucks, and 3 SUVs that it plans to display in a line across the front of the dealership.(a) In how many orders can these vehicles be displayed?(b) If the cars are grouped together at the left end of the line, in how many orders can the vehicles be displayed?
A company estimates that 30% of the country has seen its commercial and that if a person sees its commercial, there is a 20% probability that the person will buy its product. What is the probability that a person chosen at random in the country will have seen the commercial and bought the product?
Mr. Way must sell stocks from 3 of the 5 companies whose stocks he owns so that he can send his children to college. If he chooses the companies at random, what is the probability that the 3 companies will be the 3 with the best future earnings?
A newly married couple plan to have three children. Assuming that the probability of a girl being born equals that of a boy being born, what is the probability that exactly two of the three children born will be girls?
One machine produces 30% of a product for a company. If 10% of the products from this machine are defective and the other machines produce no defective items, what is the probability that an article produced by this company is defective?
The study described in Problem 47 also revealed that 91% of the men for whom the PSA test was negative do not have prostate cancer. If a man selected at random tests negative for prostate cancer with this test, what is the probability that he does have prostate cancer?
A computer store offers used computers free to local middle schools. Of the 54 machines available, four have defective memories, six others have defective keys, and the remainder have no defects. If a teacher picks one at random, what is the probability that she will select a defective computer?
To test its shotgun shells, a company fires 5 of them. What is the probability that all 5 will fire properly if 5% of the company’s shells are actually defective?
A long-term study has revealed that the prostate-specific antigen (PSA) test for prostate cancer in men is very effective. The study shows that 87% of the men for which the test is positive actually have prostate cancer. If a man selected at random tests positive for prostate cancer with this test,
The NAACP claimed that in Volusia County, Florida, police stopped dark-skinned drivers on I-95 who were not violating the law much more frequently than they stopped White drivers and then conducted searches of the cars for drugs or large sums of money that could be related to drug sales. If police
If 3% of all light bulbs a company manufactures are defective, the probability of anyone bulb being defective is 0.03. What is the probability that three bulbs drawn independently from the company’s stock will be defective?
Lactose intolerance affects about 50% of Hispanic Americans, and 9% of the residents of the United States are Hispanic. If a U.S. resident is selected at random, what is the probability that the person will be Hispanic and have lactose intolerance?
A company employs 80 people. Twenty of the 50 men and 18 of the 30 women work in the business office. What is the probability that an employee picked at random is a man or does not work in the business office?
A professor assigns 6 homework projects and then, during the next class, rolls a die to determine which one of the 6 projects to grade. If a student has completed 2 of the assignments, what is the probability that the professor will grade a project that the student has completed?
Lactose intolerance affects about 20% of non-Hispanic White Americans, and 75.6% of the residents of the United States are non-Hispanic Whites. If a U.S. resident is selected at random, what is the probability that the person will be a non-Hispanic White and have lactose intolerance?
Three construction companies have bid for a job. Max knows that the two companies with which he is competing have probabilities 1/3 and 1/6, respectively, of getting the job. What is the probability that Max will get the job?
A survey questioned 1000 people regarding lowering the legal drinking age from 21 to 19. Of the 560 who favored lowering the age, 390 were male. Of the 440 opposition responses, 160 were male. A person is selected at random.(a) What is the probability that the person is a male or favors lowering

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