Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
6th Edition
ISBN: 9781337115186
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 5.5, Problem 33E

Consider a binomial experiment with n = 20 and p = .70.

  1. a. Compute f(12).
  2. b. Compute f(16).
  3. c. Compute P(x ≥ 16).
  4. d. Compute P(x ≤ 15).
  5. e. Compute E(x).
  6. f. Compute Var (x) and σ.

a.

Expert Solution
Check Mark
To determine

Find the value of f(12).

Answer to Problem 33E

The value of f(12) is 0.1144.

Explanation of Solution

Calculation:

The binomial experiment with n=20 and p=0.70.

The probability of obtaining x successes in n independent trails of a binomial experiment is,

f(x)=(nx)px(1p)nx,x=0,1,2,...,n

Where, p is the probability of success.

Substitute values n=20 and p=0.70 and x=12.

f(12)=(2012)(0.70)12(10.70)2012=20!12!(2012)!(0.70)12(0.30)8=0.1144

Thus, the probability of 12 successes is 0.1144.

b.

Expert Solution
Check Mark
To determine

Find the value of, f(16).

Answer to Problem 33E

The value of, f(16) is 0.1304.

Explanation of Solution

Calculation:

Consider n=20 and p=0.70 and x=16.

f(16)=(2016)(0.70)16(10.70)2016=20!16!(2016)!(0.70)16(0.30)4=0.1304

Thus, the probability of 16 successes is 0.1304.

c.

Expert Solution
Check Mark
To determine

Find the value of, P(x16).

Answer to Problem 33E

The value of P(x16) is 0.2374.

Explanation of Solution

Calculation:

Here, P(x16) is the probability of at least 16 successes. This probability is the sum of the probabilities at the points x=16,x=17,x=18,x=19 and x=20. That is,

P(x16)=f(16)+f(17)+f(18)+f(19)+f(20)

The probability f(17) is obtained by substituting the values n=20 and p=0.70 and x=17 in the binomial probability formula. That is,

The probability value of f(17) is,

f(17)=(2017)(0.70)17(10.70)2017=20!17!(2017)!(0.70)17(0.30)3=0.0716

The probability value of f(18) is,

f(18)=(2018)(0.70)18(10.70)2018=20!18!(2018)!(0.70)18(0.30)2=0.0278

The probability value of f(19) is,

f(19)=(2019)(0.70)19(10.70)2019=20!19!(2019)!(0.70)19(0.30)1=0.0068

The probability value of f(20) is,

f(20)=(2020)(0.70)20(10.70)2020=20!20!(2020)!(0.70)20(0.30)0=0.0008

The required probability becomes,

P(x16)=f(16)+f(17)+f(18)+f(19)+f(20)=0.1304+0.0716+0.0278+0.0068+0.0008=0.2374

Thus, the probability of at least 16 successes is 0.2374.

d.

Expert Solution
Check Mark
To determine

Find the value of, P(x15).

Answer to Problem 33E

The value of P(x15) is 0.7626.

Explanation of Solution

Calculation:

The required probability of at most 15 successes can be obtained as the compliment of the probability of at least 15 successes. That is,

P(x15)=1P(x16)

Substituting the value from part (c),

P(x15)=1P(x16)=10.2374=0.7626

Thus, the probability of at most 15 successes is 0.7626.

e.

Expert Solution
Check Mark
To determine

Compute the expected value.

Answer to Problem 33E

The expected value of the binomial random variable is 14.

Explanation of Solution

Calculation:

The expected value of a binomial random variable is given by,

E(x)=μ=np

Substituting the values n=20 and p=0.70

E(x)=20×0.70=14

The expected value of the binomial random variable is 14.

f.

Expert Solution
Check Mark
To determine

Compute the variance and standard deviation.

Answer to Problem 33E

The variance of the binomial random variable is 4.2.

The standard deviation of the binomial random variable is 2.0494.

Explanation of Solution

Calculation:

The variance of a binomial random variable is given by,

σ2=np(1p)

Substituting the values n=20 and p=0.70

σ2=np(1p)=20×0.7(10.7)=4.2

The variance of the binomial random variable is 4.2.

The standard deviation of the random variable x is obtained by taking the square root of variance.

Thus, the standard deviation of the binomial random variable is given by,

σx=np(1p)=0.42=2.0494

The standard deviation of the binomial random variable is 2.0494.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Consider a binomial experiment with n = 20 and p = 0.70. a. Compute f(12) (to 4 decimals). b. Compute f(16) (to 4 decimals). c. Compute P(x > 16) (to 4 decimals). d. Compute P(x ≤15) (to 4 decimals). e. Compute E(x). f. Compute Var(x) (to 1 decimal) and σ (to 2 decimals). Var(x) = σ =
Consider a binomial experiment with n = 20 and p = 0.70. a. Compute f(12) (to 4 decimals). b. Compute f(16) (to 4 decimals). c. Compute P(x > 16) (to 4 decimals). d. Compute P(x ≤ 15) (to 4 decimals). e. Compute E(). f. Compute Var(x) (to 1 decimal) and a (to 2 decimals). Var(x) = J =
Consider a binomial experiment with n = 20 and p = 0.70. a. Compute f(12) (to 4 decimals). b. Compute f(16) (to 4 decimals). c. Compute P(x > 16) (to 4 decimals). d. Compute P(x < 15) (to 4 decimals). e. Compute E(x). f. Compute Var(x) (to 1 decimal) and (to 2 decimals). Var(x) = o 00

Chapter 5 Solutions

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Ch. 5.2 - 11. A technician services mailing machines at...Ch. 5.2 - 12. Time Warner Cable provides television and...Ch. 5.2 - 13. A psychologist determined that the number of...Ch. 5.2 - Prob. 14ECh. 5.3 - 15. The following table provides a probability...Ch. 5.3 - 16. The following table provides a probability...Ch. 5.3 - 17. During the summer of 2014, Coldstream Country...Ch. 5.3 - 18. The American Housing Survey reported the...Ch. 5.3 - 19. West Virginia has one of the highest divorce...Ch. 5.3 - 20. The probability distribution for damage claims...Ch. 5.3 - 21. The following probability distributions of job...Ch. 5.3 - 22. The demand for a product of Carolina...Ch. 5.3 - 23. In Gallup’s Annual Consumption Habits Poll,...Ch. 5.3 - Prob. 24ECh. 5.4 - 25. Given below is a bivariate distribution for...Ch. 5.4 - 26. A person is interested in constructing a...Ch. 5.4 - 27. The Chamber of Commerce in a Canadian city has...Ch. 5.4 - 28. PortaCom has developed a design for a...Ch. 5.4 - 29. J.P. Morgan Asset Management publishes...Ch. 5.4 - 30. In addition to the information in exercise 29...Ch. 5.5 - 31. Consider a binomial experiment with two trials...Ch. 5.5 - Prob. 32ECh. 5.5 - 33. Consider a binomial experiment with n = 20 and...Ch. 5.5 - 34. For its Music 360 survey, Nielsen Co. asked...Ch. 5.5 - 35. The Center for Medicare and Medical Services...Ch. 5.5 - 36. When a new machine is functioning properly,...Ch. 5.5 - 37. According to a 2013 study by the Pew Research...Ch. 5.5 - 38. Military radar and missile detection systems...Ch. 5.5 - 39. Market-share-analysis company Net Applications...Ch. 5.5 - 42. A Gallup Poll showed that 30% of Americans are...Ch. 5.5 - Tracked Emails. According to a 2017 Wired magazine...Ch. 5.6 - 44. Consider a Poisson distribution with μ =...Ch. 5.6 - 45. Consider a Poisson distribution with a mean of...Ch. 5.6 - 46. Phone calls arrive at the rate of 48 per hour...Ch. 5.6 - 47. During the period of time that a local...Ch. 5.6 - Prob. 48ECh. 5.6 - 49. Airline passengers arrive randomly and...Ch. 5.6 - 50. According to the National Oceanic and...Ch. 5.6 - 51. Over 500 million tweets are sent per day...Ch. 5.7 - 52. Suppose N = 10 and r = 3. Compute the...Ch. 5.7 - Prob. 53ECh. 5.7 - 54. A recent survey showed that a majority of...Ch. 5.7 - 55. Blackjack, or twenty-one as it is frequently...Ch. 5.7 - 56. Axline Computers manufactures personal...Ch. 5.7 - 57. The Zagat Restaurant Survey provides food,...Ch. 5.7 - Suppose that a shipment of 100 boxes of apples...Ch. 5 - 59. The U.S. Coast Guard (USCG) provides a wide...Ch. 5 - 60. The Car Repair Ratings website provides...Ch. 5 - 61. The budgeting process for a midwestern college...Ch. 5 - 62. A bookstore at the Hartsfield-Jackson Airport...Ch. 5 - 63. The Knowles/Armitage (KA) group at Merrill...Ch. 5 - 64. The Pew Research Center surveyed adults who...Ch. 5 - 65. The following table shows the percentage of...Ch. 5 - Prob. 66SECh. 5 - 67. PBS News Hour reported that 39.4% of Americans...Ch. 5 - Prob. 68SECh. 5 - Arrivals to a Car Wash. Cars arrive at a car wash...Ch. 5 - Prob. 70SECh. 5 - Prob. 71SECh. 5 - Prob. 72SECh. 5 - Great Grasslands Grains, Inc. (GGG) manufactures...Ch. 5 - Harriet McNeil, proprietor of McNeil’s Auto Mall,...Ch. 5 - Grievance Committee at Tuglar Corporation Several...Ch. 5 - Sagittarius Casino The Sagittarius Casino’s...
Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
Text book image
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License