(a) Explanation Given Information: The number of children in a family is 4 children and the probability that each child is a girl s 0.5. Formula used: The compliment of a probability p is, q = 1 − p Where, p is a probability of success, q is a probability of not success. The binomial distribution probability of x success in n trials is, Pr ( x ) = C n x p x q n − x Where, p is a probability of success, q is a probability of not success, n is the number of independent trials and r is desired success. Calculation: Consider a family has 4 children and the probability that each child is a girl s 0.5. p = 0.5 Use the formula for the compliment of probability p , q = 1 − p Substitute 0.5 for p . q = 1 − 0.5 = 0.5 Use the formula of binomial distribution probability, Pr ( x ) = C n x p x q n − x Substitute 0 (b) To determine To calculate: The probability that all of the children are girls if a family has 4 children and the probability that each child is a girl is 0.5.

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 8.1, Problem 15E

(a)

To determine

To calculate: The probability that half of the children are girls if a family has 4 children and the probability that each child is a girl is 0.5.

(b)

To determine

To calculate: The probability that all of the children are girls if a family has 4 children and the probability that each child is a girl is 0.5.

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Chapter 8 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 8.1 - Determine whether the following experiments...Ch. 8.1 - Prob. 2CP Ch. 8.1 - Determine whether the following experiments...Ch. 8.1 - Prob. 4CP Ch. 8.1 - 1. Suppose a fair die is rolled 18 times. (a) What...Ch. 8.1 - 2. Suppose a fair coin is tossed 12 times. (a)...Ch. 8.1 - 3. If the probability of success on each of 6...Ch. 8.1 - Prob. 4E Ch. 8.1 - 5. Suppose a fair coin is tossed 6 times. What is...Ch. 8.1 - Prob. 6E

Ch. 8.1 - 7. A fair die is rolled 12 times. What is the...Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E Ch. 8.1 - 11. Suppose a pair of dice is thrown 4 times. What...Ch. 8.1 - Prob. 12E Ch. 8.1 - 13. Suppose the probability that a marksman will...Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - 16. Testing A multiple-choice test has 10...Ch. 8.1 - 17. Management The manager of a store buys marine...Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - 22. Employee benefits In a certain school...Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - 27. Sports A baseball player has a lifetime...Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - 31. Testing A quiz consists of 10 multiple-choice...Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.2 - Prob. 1CP Ch. 8.2 - Prob. 2CP Ch. 8.2 - Prob. 3CP Ch. 8.2 - Prob. 4CP Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Prob. 11E Ch. 8.2 - Prob. 12E Ch. 8.2 - Prob. 13E Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - Prob. 21E Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Prob. 30E Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prob. 34E Ch. 8.2 - In Problems 33-36, find the mean and standard...Ch. 8.2 - Prob. 36E Ch. 8.2 - Prob. 37E Ch. 8.2 - Prob. 38E Ch. 8.2 - Assume all data are sample data. 39. Cell phones...Ch. 8.2 - Prob. 40E Ch. 8.2 - Prob. 41E Ch. 8.2 - Prob. 42E Ch. 8.2 - Prob. 43E Ch. 8.2 - Prob. 44E Ch. 8.2 - Prob. 45E Ch. 8.2 - Prob. 46E Ch. 8.2 - Prob. 47E Ch. 8.2 - Prob. 48E Ch. 8.2 - Prob. 49E Ch. 8.2 - Prob. 50E Ch. 8.2 - Prob. 51E Ch. 8.2 - Prob. 52E Ch. 8.2 - Prob. 53E Ch. 8.2 - Prob. 54E Ch. 8.3 - 1. Consider a game in which you roll a the and...Ch. 8.3 - Prob. 2CP Ch. 8.3 - Prob. 3CP Ch. 8.3 - 4. A fair cube is colored so that 4 faces are...Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Prob. 4E Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - 17. Suppose an experiment has six possible...Ch. 8.3 - Prob. 18E Ch. 8.3 - 19. Five slips of paper containing the numbers 0,...Ch. 8.3 - Prob. 20E Ch. 8.3 - 21. A die is rolled 3 times, and success is...Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - 27. Suppose a pair of dice is thrown 900 times....Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - 30. Expand Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - 37. Raffle A nonprofit organization sells chances...Ch. 8.3 - 38. Lottery A charity sells raffle tickets for $1...Ch. 8.3 - 39. Gambling Suppose a student is offered a chance...Ch. 8.3 - Prob. 40E Ch. 8.3 - Prob. 41E Ch. 8.3 - Prob. 42E Ch. 8.3 - Prob. 43E Ch. 8.3 - Prob. 44E Ch. 8.3 - Prob. 45E Ch. 8.3 - Prob. 46E Ch. 8.3 - Prob. 47E Ch. 8.3 - 48. Cancer research Suppose it has been determined...Ch. 8.3 - 49. Voting A candidate claims that 60% of the...Ch. 8.3 - Prob. 50E Ch. 8.3 - Prob. 51E Ch. 8.3 - Prob. 52E Ch. 8.3 - 53. Quality control A certain calculator circuit...Ch. 8.3 - Prob. 54E Ch. 8.3 - Prob. 55E Ch. 8.3 - 56. Quality control The probability that a...Ch. 8.3 - 57. Oil drilling Suppose that when an oil company...Ch. 8.3 - Prob. 58E Ch. 8.4 - 1. The mean of a normal distribution is 25, and...Ch. 8.4 - Prob. 2CP Ch. 8.4 - 3. For the normal distribution with mean 70 and...Ch. 8.4 - Prob. 1E Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - Prob. 10E Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Suppose a population of scores x is normally...Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - 28. Find the number A that satisfies for the...Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - 31. Growth The Fish Commission states that the...Ch. 8.4 - Prob. 32E Ch. 8.4 - Prob. 33E Ch. 8.4 - 34. Mating calls The durations of the mating calls...Ch. 8.4 - Prob. 35E Ch. 8.4 - 36. Testing The Scholastic Aptitude Test (SAT)...Ch. 8.4 - 37. Mileage A certain model of automobile has its...Ch. 8.4 - Prob. 38E Ch. 8.4 - 39. Blood pressure Systolic blood pressure for a...Ch. 8.4 - Prob. 40E Ch. 8.4 - Prob. 41E Ch. 8.4 - Prob. 42E Ch. 8.4 - Prob. 43E Ch. 8.4 - Prob. 44E Ch. 8.4 - Prob. 45E Ch. 8.4 - Prob. 46E Ch. 8.4 - Prob. 47E Ch. 8.5 - Prob. 1CP Ch. 8.5 - Prob. 2CP Ch. 8.5 - Prob. 1E Ch. 8.5 - Prob. 2E Ch. 8.5 - Prob. 3E Ch. 8.5 - Prob. 4E Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - Prob. 6E Ch. 8.5 - Prob. 7E Ch. 8.5 - Prob. 8E Ch. 8.5 - Prob. 9E Ch. 8.5 - Prob. 10E Ch. 8.5 - Prob. 11E Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - Prob. 13E Ch. 8.5 - Prob. 14E Ch. 8.5 - Prob. 15E Ch. 8.5 - Prob. 16E Ch. 8.5 - Prob. 17E Ch. 8.5 - Prob. 18E Ch. 8.5 - Prob. 19E Ch. 8.5 - Prob. 20E Ch. 8.5 - Prob. 21E Ch. 8.5 - Prob. 22E Ch. 8.5 - Prob. 23E Ch. 8.5 - Prob. 24E Ch. 8.5 - Prob. 25E Ch. 8.5 - Prob. 26E Ch. 8.5 - Prob. 27E Ch. 8.5 - Prob. 28E Ch. 8.5 - Prob. 29E Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - Prob. 31E Ch. 8.5 - Prob. 32E Ch. 8.5 - Prob. 33E Ch. 8.5 - Prob. 34E Ch. 8.5 - Prob. 35E Ch. 8.5 - Prob. 36E Ch. 8.5 - Prob. 37E Ch. 8.5 - Prob. 38E Ch. 8 - 1. If the probability of success on each trial of...Ch. 8 - Prob. 2RE Ch. 8 - 3. If a die is rolled 4 times, what is the...Ch. 8 - Prob. 4RE Ch. 8 - Prob. 5RE Ch. 8 - Prob. 6RE Ch. 8 - Prob. 7RE Ch. 8 - Prob. 8RE Ch. 8 - Prob. 9RE Ch. 8 - Prob. 10RE Ch. 8 - Prob. 11RE Ch. 8 - Prob. 12RE Ch. 8 - Prob. 13RE Ch. 8 - Prob. 14RE Ch. 8 - Determine whether each function or table in...Ch. 8 - Prob. 16RE Ch. 8 - Prob. 17RE Ch. 8 - Prob. 18RE Ch. 8 - Prob. 19RE Ch. 8 - Prob. 20RE Ch. 8 - Prob. 21RE Ch. 8 - Prob. 22RE Ch. 8 - Prob. 23RE Ch. 8 - Prob. 24RE Ch. 8 - Prob. 25RE Ch. 8 - Prob. 26RE Ch. 8 - Prob. 27RE Ch. 8 - Prob. 28RE Ch. 8 - Prob. 29RE Ch. 8 - Prob. 30RE Ch. 8 - Prob. 31RE Ch. 8 - Prob. 32RE Ch. 8 - Prob. 33RE Ch. 8 - Prob. 34RE Ch. 8 - Prob. 35RE Ch. 8 - Prob. 36RE Ch. 8 - Prob. 37RE Ch. 8 - Prob. 38RE Ch. 8 - 39. Sampling Suppose of a population opposes a...Ch. 8 - Prob. 40RE Ch. 8 - 41. Disease One person in 100,000 develops a...Ch. 8 - Prob. 42RE Ch. 8 - Prob. 43RE Ch. 8 - Prob. 44RE Ch. 8 - Prob. 45RE Ch. 8 - 46. Fraud A company selling substandard drugs to...Ch. 8 - Prob. 47RE Ch. 8 - Prob. 48RE Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - 51. Net worth Suppose the mean net worth of the...Ch. 8 - 52. Testing The length of time it takes to...Ch. 8 - Prob. 53RE Ch. 8 - Prob. 54RE Ch. 8 - Prob. 55RE Ch. 8 - Prob. 56RE Ch. 8 - Prob. 1T Ch. 8 - Prob. 2T Ch. 8 - Prob. 3T Ch. 8 - Prob. 4T Ch. 8 - Prob. 5T Ch. 8 - Prob. 6T Ch. 8 - 7. If the variable x is normally distributed, with...Ch. 8 - Prob. 8T Ch. 8 - Prob. 9T Ch. 8 - Prob. 10T Ch. 8 - Prob. 11T Ch. 8 - Prob. 12T Ch. 8 - Prob. 13T Ch. 8 - Prob. 14T Ch. 8 - Prob. 15T Ch. 8 - Prob. 16T Ch. 8 - Prob. 17T Ch. 8 - Prob. 18T Ch. 8 - Prob. 19T Ch. 8 - Prob. 20T Ch. 8 - Prob. 21T Ch. 8 - Prob. 22T Ch. 8 - Prob. 1EAGP1 Ch. 8 - Prob. 2EAGP1

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The probability that half of the children are girls if a family has 4 children and the probability that each child is a girl is 0.5.

Solution Summary: The author explains how to calculate the probability that half of the children are girls if a family has 4 children.

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To calculate: The probability that half of the children are girls if a family has 4 children and the probability that each child is a girl is 0.5.

To calculate: The probability that all of the children are girls if a family has 4 children and the probability that each child is a girl is 0.5.

Chapter 8 Solutions