Mathematics, 29.02.2020 01:15 kazmiere2005oye9tz

Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev's theorem to determine the minimum percentage of the data within each of the following ranges. (Round your answers to the nearest integer.) (a) 20 to 40 % (b) 15 to 45 % (c) 23 to 37 % (d) 17 to 43 % (e) 13 to 47

Answers: 2

Show answers

Answers

a) We are within 2 deviations from the mean since 30 -2*5 = 20 and 30 + 2*5 = 40. So our value for k = 2 and we can find the % like this:

$\% = (1- \frac{1}{2^2}) *100 = 75\%$

b) We are within 3 deviations from the mean since 30 -3*5 = 20 and 30 + 3*5 = 45. So our value for k = 3 and we can find the % like this:

$\% = (1- \frac{1}{3^2}) *100 = 88.88\% \approx 89\%$

c) We are within 1.4 deviations from the mean since 30 -1.4*5 = 23 and 30 + 1.4*5 = 37. So our value for k = 1.4 and we can find the % like this:

$\% = (1- \frac{1}{1.4^2}) *100 = 48.97\% \approx 49\%$

d) We are within 2.6 deviations from the mean since 30 -2.6*5 = 17 and 30 + 2.6*5 = 43. So our value for k = 2.6 and we can find the % like this:

$\% = (1- \frac{1}{2.6^2}) *100 = 85.2\% \approx 85\%$

e) We are within 3.4 deviations from the mean since 30 -3.4*5 =13 and 30 + 3.4*5 = 47. So our value for k = 3.4 and we can find the % like this:

$\% = (1- \frac{1}{3.4^2}) *100 = 91.35\% \approx 91\%$

Step-by-step explanation:

For this case we need to remember what says the Chebysev theorem, and it says that we have at least $1-\frac{1}{k^2}$ of the data liying within k deviations from the mean on the interval $\bar X \pm k s$

We know that $\bar X= 30, s=5$

Part a

For this case we want the values between 20 and 40

So we are within 2 deviations from the mean since 30 -2*5 = 20 and 30 + 2*5 = 40. So our value for k = 2 and we can find the % like this:

$\% = (1- \frac{1}{2^2}) *100 = 75\%$

Part b

For this case we want the values between 15 and 45

So we are within 3 deviations from the mean since 30 -3*5 = 20 and 30 + 3*5 = 45. So our value for k = 3 and we can find the % like this:

$\% = (1- \frac{1}{3^2}) *100 = 88.88\% \approx 89\%$

Part c

For this case we want the values between 23 and 37

So we are within 1.4 deviations from the mean since 30 -1.4*5 = 23 and 30 + 1.4*5 = 37. So our value for k = 1.4 and we can find the % like this:

$\% = (1- \frac{1}{1.4^2}) *100 = 48.97\% \approx 49\%$

Part d

For this case we want the values between 17 and 43

So we are within 2.6 deviations from the mean since 30 -2.6*5 = 17 and 30 + 2.6*5 = 43. So our value for k = 2.6 and we can find the % like this:

$\% = (1- \frac{1}{2.6^2}) *100 = 85.2\% \approx 85\%$

Part e

For this case we want the values between 13 and 47

So we are within 3.4 deviations from the mean since 30 -3.4*5 =13 and 30 + 3.4*5 = 47. So our value for k = 3.4 and we can find the % like this:

$\% = (1- \frac{1}{3.4^2}) *100 = 91.35\% \approx 91\%$

Answer from: Quest

Dfitjngjgngnfjgjtngjgjnggjgjgngngnjg
What are the y-intercept and the slope of the line represented in the graph? a. y-intercept = -4 and

Answer from: Quest

C. i possibility the answer to this

Another question on Mathematics

Mathematics, 21.06.2019 16:30

In two or more complete sentences describe how to determine the appropriate model for the set of data, (1,1), (3,2), (6,3), (11,4).

Answers: 1

Answer

Mathematics, 21.06.2019 16:30

One of the same side angles of two parallel lines is 20° smaller than the other one. find the measures of these two angles.

Answers: 3

Answer

Mathematics, 21.06.2019 18:00

Given: and prove: what is the missing reason in the proof? given transitive property alternate interior angles theorem converse alternate interior angles theorem

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

0if x and y vary inversely and y=6 as x=7, what is the constant of variation?

Answers: 1

Answer

You know the right answer?

Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev's theorem to determ...

Questions