1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Arisa [49]
3 years ago
13

The results of a national survey showed that on average, adults sleep 6.3 hours per night. Suppose that the standard deviation i

s 1.6 hours. (a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.1 and 9.5 hours. % (b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 2.3 and 10.3 hours. % (c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 3.1 and 9.5 hours per day. % How does this result compare to the value that you obtained using Chebyshev's theorem in part (a)
Mathematics
1 answer:
alekssr [168]3 years ago
8 0

Answer:

a) 75%.

b) 84%

c) Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Chebyshev Theorem:

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by 100(1 - \frac{1}{k^{2}}).

In this question:

Mean: 6.3 hours

Standard deviation: 1.6 hours

(a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.1 and 9.5 hours.

3.1 = 6.3 - 2*1.6

9.5 = 6.3 + 2*1.6

Within 2 standard deviations, so the minimum percentage is 75%.

(b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 2.3 and 10.3 hours.

How many standard deviations from the mean?

One standard deviation is 1.6

These measures are 10.3 = 6.3 = 6.3 - 2.3 = 4. This is k standard deviations, in which

k = \frac{4}{1.6} = 2.5

The minimum percentage is:

100(1 - \frac{1}{k^{2}}) - 100(1 - \frac{1}{2.5^{2}}) = 84%

So 84%.

(c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 3.1 and 9.5 hours per day.

Within 2 standard deviations from the mean is 95%. The normal distribution has a higher percentage of observations closer to the mean than a non normal distribution, so this percentage is larger.

You might be interested in
How are the coordinates of the extreme value and the equation from part B in the form y=(x-h)^2-c related.
True [87]

The extreme value of y = (x - h)² - c is the vertex of the equation.

<h3>What are extreme values of a function?</h3>

The extreme values of a function are either the maximum or minimum values of the function.

<h3>The equation of a parabola in vertex form</h3>

The equation of a parabola in vertex form with vertex (h', k) is given by

y = a(x - h')² + k and its extreme values are

  • if a > 0  (h', k) is a minimum point and
  • if a < 0 (h', k) is a maximum point.

Since y = (x - h)² - c is the equation of a parabola in vertex form, comparing with y = a(x - h')² + k,

  • h = h'
  • -c = k and
  • a = 1.

So, the cooordinates of the vertex of y = (x - h)² - c is (h, -c).

Now, since a = 1 > 0, (h, -c) is a minimum point.

So, the extreme value of y = (x - h)² - c is the vertex of the equation.

Learn more about extreme value of a function here:

brainly.com/question/13464558

#SPJ1

4 0
2 years ago
Which expressions are equivalent to 2r+(t+r)
irga5000 [103]

Answer:

Option C -> None of the above.

Step-by-step explanation:

Given-

2 r + ( t + r )

<em>⇒ 2 r + t + r</em>

<em>⇒ 2 r + r + t</em>

<em>⇒ 3 r + t</em>

∵ 2 r + ( t + r ) = 3 r + t.

∴ The given expression is equivalent to Option C : None of the above.

8 0
3 years ago
Read 2 more answers
Write 95.417 in expanded form with multiplication
Svetllana [295]
In expanded form, it would be 9*10 + 5*1 + 4 * 0.1 + 1 * 0.01 + 7 * 0.001. Hope this helps!
6 0
2 years ago
Please help is for now
cupoosta [38]
3 because I did the quiz and got it right txt me if you need help
8 0
3 years ago
Read 2 more answers
Find the area. The figure is not drawn to scale.
jeka94

Answer:

627,264 square inches

Step-by-step explanation:

multiply all the numbers together

5 0
3 years ago
Other questions:
  • If 3x-7=5t what is 6t?
    14·1 answer
  • Parminder is working at an isolated weather station in the Yukon. She earns an annual salary of $45 650.00 plus $780.00/month fo
    9·1 answer
  • Susan is looking into a new cell phone carrier. She researches her options and finds the two companies which off the best recept
    11·1 answer
  • The figure are similar find x
    5·1 answer
  • Will 50,48 and 14 form a right triangle​
    8·2 answers
  • [geometry] i got 267.94 but how do i answer that in fraction?
    11·1 answer
  • PLEASE ANSWER ASASP FOR BRAINLEST!!!!!!!!!!!!!!
    10·1 answer
  • Kayla went deep sea fishing. She cast her line 15 feet underneath the water. Which number best represents this integer?
    15·1 answer
  • Solve this question Find AC​
    10·1 answer
  • Find the monthly house payment necessary to amortize the following loan. In order to purchase a home, a family borrows $110,000
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!