Americans spend an average of 3 hours per day online. If the standard deviation is 32 minutes, find the range in which at least 88.89% of the data will lie. Use Chebyshev's theorem. Hint: You should memorize that when k is 2, it is 75% and when k is 3 it is 88.89%. Also convert hours to minutes and state your answer in minutes.

Answers

Answer 1

Answer:

84 minutes to 276 minutes

Step-by-step explanation:

Chebyshev's theorem states that:

At least 3/4(75% ) of data falls within 2 standard deviation from the mean - that means between μ - 2σ and μ + 2σ

At least 8/9(88.89)% of data falls within 3 standard deviations from the mean - between μ – 3σ and μ + 3σ .

Where k > 1 , 1 - 1/k²

k is 2, it is 75% and when k is 3 it is 88.89%

Americans spend an average of 3 hours per day online. If the standard deviation is 32 minutes, find the range in which at least 88.89% of the data will lies

Step 1

Convert 3 hours to minutes

1 hour = 60 minutes

3 hours = x

Cross Multiply

= 3hours × 60 minutes/1 hour

= 180 minutes

We know from Chebyshev's theorem that:

At least 8/9(88.89)% of data falls within 3 standard deviations from the mean - between μ – 3σ and μ + 3σ .

Hence

μ = 180 minutes, σ =32 minutes

μ – 3σ

= 180 - 3(32)

= 180 - 96

= 84 minutes

μ + 3σ

= 180 + 3(32)

= 180 + 96

= 276 minutes

Therefore the range in which at least 88.89% of the data will lie is 84 minutes to 276 minutes


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Step-by-step explanation:

On a 28-question test, there are 2-point questions, 4-point questions, and 5-point questions. The test is worth a total of 100 points. There are twice as many 2-point questions as 5-point questions on the test. How many 2-point questions are on the test?

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Answer

Answer: Number of 5-point question = 4

Number of 2-point questions =8

Number of 4-point question = 16

Step-by-step explanation:

Let x = Number of 5-points question.

then, Number of 2- point question = 2x

Also, Let y = Number of 4-point question.

Now, Total question : x+y+2x =28

⇒ 3x+ y =28    (i)

Total marks = 5x + 2 (2x)+4=100

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⇒ 9x+4y=100     (ii)

Multiply 3 on both sides of (i), we get

9x+3y = 84    (iii)

Subtract (iii) from (ii), we get

y= 16

Put this in (i0, we get

3x+(16)=28

⇒ 3x = 12

⇒ x=4

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negative 5 over 32 degrees Fahrenheit

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Given the following :

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