Each statement represents a scenario in which a linear transformation has occurred. Select the correct statements...

Each statement represents a scenario in which a linear transformation has occurred. Select the correct statements regarding the standard deviation of the variables after the linear transformation.

-A malfunctioning machine produces a particular part with a mean length of 30 in and a standard deviation of 1 in. If a second part with a consistent length of 2 in is added to the end of the first part, then the standard deviation of the total part lengths will be equal to 3 in.

-The distribution of heights of adult males in the United States has a standard deviation of 4 in. If these heights in inches are converted to feet, then the standard deviation of heights will be 13 ft.

-Prices on a menu at a particular restaurant have a mean cost of $10 and a standard deviation of $4. If the restaurant decides to raise its prices by 50%, then the standard deviation of the new prices will be $6.

-For a particular set of daily TV-watching data, the average number of hours of TV watched per day is 3 hrs, and the standard deviation is 2 hrs. If these daily results are translated to weekly TV-watching results, the standard deviation for the total number of hours of TV watched per week remains unchanged from the standard deviation of 2 hrs.

-The final times (in minutes) for a high school foot race are distributed with a mean of 20 min and a standard deviation of 4 min. The person charged with keeping track of time realized that he started the stopwatch 1 minlate for all runners. Thus, he decides to add 1 min to everyone's time. The standard deviation of the new final times will remain unchanged at 4 min.

Solutions

Expert Solution

#1 ) Incorrect.

Standard deviation influenced by outliers one value could contribute largely to the results of the standard deviation.

We are given that the average of first part is 30inches, it means most of part lengths are close to 30inches. Therefore If a second part with a consistent length of 2 in is added to the end of the first part, it would be work as an outlier, so the standard deviation of the total part lengths will be large.

#2) Incorrect , The standard deviation of heights will be 4*12 =48 ft ( standard deviation is only affected by a change in scale.)

#3) Correct !.

Since standard deviation is only affected by a change in scale , so raise in prices by 50% means we have to multiply by 0.5 to the standard deviation and add that product to the standard deviation , it will give the new standard deviation after rasing the prices by 50%

So 0.5*$4 = $2 , $4+$2 = $6

#4) Incorrect .

If these daily results are translated to weekly TV-watching results,then we need to multiply by standard deviation by 7 ( 7 days in a week )

So standard deviation = 2*7 = 14 hrs

$5) Correct!

standard deviation is only affected by a change in scale ( multiplication and division ) and not by the change of origin ( adding or subtracting ) .

milcah answered 3 weeks ago

Next > < Previous

Related Solutions

47. Which of the following statements are correct? Select which option is correct. Select one or...

47. Which of the following statements are correct? Select which option is correct. Select one or more: The level of professional skepticism can be reduced where the auditor has past experience with the entity indicating the honesty and integrity of management. The level of professional skepticism needs to be maintained throughout the whole engagement. Professional skepticism implies an expectation of fraud or error, so is a biased viewpoint. Professional skepticism is not important in considering management's explanations for unusual trends...

Let T : Rn -> Rm be a onto linear transformation. Select all the true statements...

Let T : Rn -> Rm be a onto linear transformation. Select all the true statements from the following list. (Incorrect choices will earn you negative points) For any y in Rm there exists a unique x in Rn such that T(x) = y For any y in Rm there is at most one x in Rn such that T(x) = y The range of T is the entire Rm For any y in Rm there is at least one...

Which of the following represents the correct order in which the FASB develops Statements of Financial...

Which of the following represents the correct order in which the FASB develops Statements of Financial Accounting Standards? Multiple Choice public heaings, discussion memorandum, exposure draft, vote exposure draft, discussion memorandum, public hearings, vote discussion memorandum, public hearings, exposure draft, vote discussion memorandum, exposure draft, public hearings, vote

Which of the following statements is true? Select the correct answer a.NONE OF THE STATEMENTS ARE...

Which of the following statements is true? Select the correct answer a.NONE OF THE STATEMENTS ARE TRUE b.Electric forces depend on velocity of a charged object c.Objects having a net charge experience only electric force, not magnetic force d.It is impossible to separate the North and South poles of a bar magnet e.Electric forces decrease with decreasing distance from charges, but magnetic forces do not decrease with decreasing distance from magnets

Which of the following statements are correct (Select all that apply): Select one or more: A....

Which of the following statements are correct (Select all that apply): Select one or more: A. An income statement reports on financing activities. B. A balance sheet reports on investing and financing activities. C. The statement of cash flows reports on cash flows from operating, investing, and financing activities over a period of time. D. A balance sheet reports on a company's assets and liabilities over a period of time. E. The statement of equity reports on changes in the...

Which of the following statements are correct (Select all that apply): Select one or more: A....

Which of the following statements are correct (Select all that apply): Select one or more: A. A balance sheet reports on investing and financing activities. B. An income statement reports on financing activities. C. The statement of equity reports on changes in the accounts that make up equity. D. The statement of cash flows reports on cash flows from operating, investing, and financing activities over a period of time. E. A balance sheet reports on a company's assets and liabilities...

Which of the following statements is true? Select the correct answer below: The U.S. economy has...

Which of the following statements is true? Select the correct answer below: The U.S. economy has had persistent trade surpluses since the 1970s A large measure of exports as a percentage of GDP indicates large levels of globalization in a country. If exports as a percentage of GDP are low, then a large trade deficit will not have a huge impact on a country's economy. It is better for a country to have large exports as a percentage of GDP.

Which of the following statements is correct? Select one: a. A line of credit is an...

Which of the following statements is correct? Select one: a. A line of credit is an agreement between a bank and a customer under which the bank guarantees the customer a fixed dollar amount of loan. b. Banks issue commercial paper for raising funds for long periods c. Securitisation of loans reduces banks’ capital requirements. d. The principal source of funds for banks is through the issue of debt securities.

Which statements regarding indole production in SIM test is correct? select all correct statements. Tryptophanase hydrolyzes...

Which statements regarding indole production in SIM test is correct? select all correct statements. Tryptophanase hydrolyzes tryptophan into indole and pyruvate Pyruvate reacts with ferrous sulfate in the media producing a black percipitate Non-motile organisms will only show the color change along the stab line. Indole can be detected by the addition of Kovac's reagent

Which of the following statements regarding prospecting theory is true? Explain why each statement is correct...

Which of the following statements regarding prospecting theory is true? Explain why each statement is correct or incorrect. a. Certainty is given low weight relative to near-certainty. b. Prospect theory weights are exactly the same as the probabilities used in Expected Utility Theory. c. The weighting function for losses can differ from the weighting function for gains. d. A gains adds more to utility than an equal-sized loss subtracts from it.

Subjects