Question

The following data represent the number of touchdown passes thrown by a particular quarterback during his first 18 seasons. Verify that​ Chebyshev's Theorem holds true by determining the percent of observations that fall within

plus or minus±​one,

​two, and three standard deviations from the mean.

00	1919	1616	3333	4040	3737	3131	3333	2222
2020	3434	2727	3434	3232	1717	1919	2929	2525

What is the mean of the data​ set?

x overbar=

​(Type an integer or decimal rounded to two decimal places as​ needed.)

What is the standard deviation of the data​ set?

s=

​(Round to two decimal places as​ needed.)

Calculate the interval

x overbarxplus or minus±s.

x overbarxplus or minus±=( , )

​(Round to two decimal places as needed. Type your answer in interval​ notation.)

What percentage of the data values fall within the interval

x overbarxplus or minus±​s?

The percentage of data values that fall within the interval is

nothing​%

​(Round to the nearest percent as​ needed.)

Calculate the interval

x overbarxplus or minus±2s.

x overbarxplus or minus±2sequals=left parenthesis nothing comma nothing right parenthesis,

​(Round to two decimal places as needed. Type your answer in interval​ notation.)

What percentage of the data values fall within the interval

x overbarxplus or minus±​2s?

That percentage of data values that fall within the interval is

nothing​%

​(Round to the nearest percent as​ needed.)

Calculate the interval

x overbarxplus or minus±3s.

x overbarxplus or minus±3sequals=left parenthesis nothing comma nothing right parenthesis,

​(Round to two decimal places as needed. Type your answer in interval​ notation.)

What percentage of the data values fall within the interval

x overbarxplus or minus±​3s?

That percentage of data values that fall within the interval is

nothing​%

​(Round to the nearest percent as​ needed.)

Do these percentages agree with​ Chebyshev's Theorem?

A.The percentage for

x overbarxplus or minus±2s

does not agree with​ Chebyshev's Theorem.

B.

All the percentages agree with​ Chebyshev's Theorem.

C.The percentage for

x overbarxplus or minus±3s

does not agree with​ Chebyshev's Theorem.

D.

None of the percentages agree with​ Chebyshev's Theorem.

Answer 1

Given Data

Data	0	19	16	33	40	37	31	33	22
	20	34	27	34	32	17	19	29	25

Mean = = 26.00

Std dev s = = 9.77

s = ( - s , + s) = (26 - 9.77 , 26 + 9.77) = ( 16.23, 35.77)

14 observations are there in this range that will be 100*14/18 = 78%

2s = ( - 2s , + 2s) = (26 - 2*9.77 , 26 + 2*9.77) = ( 6.46 , 45.54)

17 observations are there in this range that will be 100*17/18 = 94%

3s = ( - 3s , + 3s) = (26 - 3*9.77 , 26 + 3*9.77) = ( -3.31 , 55.31)

18 observations are there in this range that will be 100*18/18 = 100%

Do these percentages agree with​ Chebyshev's Theorem?

D.

None of the percentages agree with​ Chebyshev's Theorem.

As per the chebyshev's theorem percent of the data will lie in the k std dev.

for k =1 percentage = 0

for k = 2 percentage = 75%

for k = 3 percentage = 89%

for the given data None of the percentages agree with​ Chebyshev's Theorem.