Internal auditors are often used to review an organization's financial statements such as balance sheets, income statements, and cash flow statements prior to public filings. Auditors seek to verify that the financial statements accurately represent the financial position of the organization and that the statements follow accepted accounting principles. Many errors that are discovered by auditors are minor errors that are easily corrected. However, some errors are serious and require substantial time to rectify. Suppose that the financial statements of 567 public companies were audited. The file internalaudit3.xlsx contains the number of serious errors discovered during the internal audit of each of these 567 public companies that were classified as \"serious errors.\" Use the data in the file internalaudit3.xlsx to answer the following. (a) Construct an empirical discrete probability distribution for the number of serious errors discovered during the internal audits of these 567 public companies. (Round your answers to five decimal places.) Number of Serious Errors Probability $f(x)$ 0 0.17284 1 0.07780 2 0.00171 3 0.41270 4 0.15873 5 0.01235 6 0.07407 (b) What is the probability that a company has no serious errors in its financial statements? (Round your answer to five decimal places.) 0.17284 (c) What is the probability that a company has four or more serious errors in its financial statements? (Round your answer to five decimal places.) 0.24515 (d) What is the expected number of serious errors in a company's financial statements? (Round your answer to four decimal places.) 1.8764 (e) What is the variance of the number of serious errors in a company's financial statements? (Round your answer to four decimal places.) 2.5926 (f) What is the standard deviation of the number of serious errors in a company's financial statements? (Round your answer to four decimal places.) 1.3552
Added by George L.
Close
Step 1
Step 1: Read the text carefully to identify any errors or issues. Show more…
Show all steps
Your feedback will help us improve your experience
Clarissa Barr and 92 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
According to an airline, flights on a certain route are on time 80% of the time. Suppose 15 flights are randomly selected and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Find and interpret the probability that exactly 10 flights are on time. (c) Find and interpret the probability that fewer than 10 flights are on time. (d) Find and interpret the probability that at least 10 flights are on time. (e) Find and interpret the probability that between 8 and 10 flights, inclusive, are on time. (a) Identify the statements that explain why this is a binomial experiment. Select all that apply. A. There are two mutually exclusive outcomes, success or failure. B. The probability of success is the same for each trial of the experiment. C. Each trial depends on the previous trial. D. The trials are independent. E. There are three mutually exclusive possibly outcomes, arriving on-time, arriving early, and arriving late. F. The experiment is performed a fixed number of times. G. The experiment is performed until a desired number of successes is reached. (b) The probability that exactly 10 flights are on time is []. (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected about [] to result in exactly 10 flights being on time. (Round to the nearest whole number as needed.) (c) The probability that fewer than 10 flights are on time is []. (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected about [] to result in fewer than 10 flights being on time. (Round to the nearest whole number as needed.) (d) The probability that at least 10 flights are on time is []. (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected about [] to result in at least 10 flights being on time. (Round to the nearest whole number as needed.) (e) The probability that between 8 and 10 flights, inclusive, are on time is []. (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected about [] to result in between 8 and 10 flights, inclusive, being on time. (Round to the nearest whole number as needed.)
Clarissa B.
A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 70 industrial firms. An inspector will visit 10 randomly selected firms to check for violations of regulations. (a) If 28 of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by the inspector that are in violation of at least one regulation? b(x; 10, 28, 70) nb(x; 10, 0.4) nb(x; 10, 28, 70) b(x; 10, 0.4) h(x; 10, 0.4) h(x; 10, 28, 70) (b) If there are 700 firms in the area, of which 280 are in violation, approximate the pmf of part (a) by a simpler pmf. b(x; 10, 280, 700) h(x; 10, 280, 700) h(x; 10, 0.4) b(x; 10, 0.4) nb(x; 10, 280, 700) nb(x; 10, 0.4) (c) For X = the number that are in violation among the 10 visited out of 700 firms, compute E(X) and V(X) both for the exact pmf and the approximating pmf in part (b). (Round your answers to two decimal places.) Compute E(X) and V(X) for the exact pmf. E(X) = 4 V(X) = 2.4 Compute E(X) and V(X) for the approximating pmf. E(X) = 4 V(X) = 2.4
Jon S.
The company considers a component to be "successful" if it lasts longer than the warranty period before failing. They estimate that about 70.3% of components last more than 4 years. They find a random group of 10 components that were sold and count the number of them which were "successful," lasting more than 4 years. a. What is the expected number of these 10 components that will last more than 4 years? (Round your answer to 1 decimal place.) (3 pt) b. What is the standard deviation for the number of these 10 components that will last more than 4 years? (Round your answer to 1 decimal place.) (3 pt) c. What is the probability that at least 8 of these components will last more than 4 years? (3 pt) d. What is the probability that no more than 6 of these components will last more than 4 years? (3 pt) 12. The company is not satisfied with how many returns they are processing, and accountants in the company are recommending that they change the warranty period. The accountants suggest basing the period of the warranty on making sure, in the long run, only about 5% of customers will return the component. What amount of time corresponds to the shortest 5% of lifespans for this component? (Round your answer to 1 decimal place.) (4 pt) 13. A journalist believes that, in reality, these components have a shorter lifespan than what the company is reporting. He tests a random group of 35 of these components and finds a mean lifespan of 4.05 years. a. What is the mean of the sampling distribution of sample means when 35 random components are tested? (2 pt) b. What is the standard error of the sampling distribution when 35 random components are tested? (2 pt) c. If the company's reported lifespan distribution were really true, what is the probability that a random group of 35 will have a sample mean lifespan of 4.05 years or less? (4 pt) d. Would this be a significant result? (Choose one.) (4 pt) A. Yes B. No C. Not enough information
Patha S.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD