Mathematics, 20.02.2020 06:07 jocelynmarquillo1

Americans spend an average of 3 hours per day online. If the standard deviation is 32 minutes, use Chebyshevs theorm to find the range (in minutes) which at least 93.75% of Americans spend online. Fine the z score for an online time of 4.75 hours per day

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Answer from: pulidoshorty

$0.9375 = 1- \frac{1}{k^2}$

$\frac{1}{k^2} = 1-0.9375=0.0625$

$k = \sqrt{\frac{1}{0.0625}}= 4$

So then the range would be given by:

$Lower = \mu -4 \sigma = 180 -4*32=52 min$

$Upper = \mu +4 \sigma = 180 +4*32=308min$

x =4.75*60= 285 min we got:

$z = \frac{285-180}{32}=3.281$

So this value means that 4.75 hr = 285 min is a value approximately 3.3 deviations above the mean of the distribution.

Step-by-step explanation:

For this case we have the following data given:

$\mu = 3*60 = 180 min$ represent the mean

$\sigma= 32min$ represent the deviation

The Chebysev theorem states that we have at least $1- \frac{1}{k^2}$ of the data lying withink k standard deviations of the mean.

So for this case we want 93.75% of the data or 0.9375 if we find the value of k we got:

$0.9375 = 1- \frac{1}{k^2}$

$\frac{1}{k^2} = 1-0.9375=0.0625$

$k = \sqrt{\frac{1}{0.0625}}= 4$

So then the range would be given by:

$Lower = \mu -4 \sigma = 180 -4*32=52 min$

$Upper = \mu +4 \sigma = 180 +4*32=308min$

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

The z score is given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we replace for x =4.75*60= 285 min we got:

$z = \frac{285-180}{32}=3.281$

So this value means that 4.75 hr = 285 min is a value approximately 3.3 deviations above the mean of the distribution.

Answer from: Quest

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200. after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes 1800 - 6400 which gets you 11,600.

Answer from: Quest

x is greater than 5

step-by-step explanation:

2x+7 is greater than 17

-7 -7

2x is greater than 10

divide by 2 each side

x is greater than 5

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Americans spend an average of 3 hours per day online. If the standard deviation is 32 minutes, use C...