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ikadub [295]
3 years ago
8

An article reported that the mean annual adult consumption of wine was 3.85 gallons and that the standard deviation was 6.07 gal

lons. Would you use the empirical rule to approximate the proportion of adults who consume more than 9.92 gallons (i.E., the proportion of adults whose consumption value exceeds the mean by more than 1 standard deviation)? Explain your reasoning. (Round your numerical answer to three decimal places.)
Mathematics
1 answer:
Komok [63]3 years ago
5 0

Answer:

0.159 is the required proportion.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 3.85 gallons

Standard Deviation, σ = 6.07 gallons

We are given that the distribution of consumption of wine is a bell shaped distribution that is a normal distribution.

Empirical Formula:

  • Almost all the data lies within three standard deviation from the mean for a normally distributed data.
  • About 68.2% of data lies within one standard deviation from the mean.
  • About 95% of data lies within two standard deviations of the mean.
  • About 99.7% of data lies within three standard deviation of the mean.

We have to evaluate:

=P(x \geq 9.92)\\=P(x \geq \mu + 1(\sigma))\\=0.5 - \dfrac{1}{2}(0.68.2)\\\\=0.5 - 0.34\\=0.159

0.159 is the proportion of adults whose consumption value exceeds the mean by more than 1 standard deviation.

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NikAS [45]
<h3>Answer:  20% increase</h3>

======================================================

Explanation:

A = old value = 110

B = new value = 132

C = percent change

C = 100*(B-A)/A

C = 100*(132-110)/110

C = 20%

The positive C value means we have a percent increase, which corresponds to the fact that A = 110 increases to B = 132.

The B-A = 132-110 = 22 portion up top indicates that the increase is 22 pounds, which when divided over 110, gets us 22/110 = 0.20 = 20%

---------------

Checking the answer:

20% of 110 = 0.20*110 = 22

She's able to lift 22 extra pounds on top of the 110 pounds she can handle previously, so she can now lift 110+22 = 132 pounds. The answer is confirmed.

7 0
2 years ago
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The scatter plot shows the amount of sleep Aria got the night before a test and her test scores. Use the y-intercept, (0, 62), a
kotegsom [21]

Answer:

y = 3x + 62

Step-by-step explanation:

Trend line equation in the form :

y = mx + b

m = slope

b = intercept

Using the points :

(0, 62) ; (6, 80)

Slope, m = Rise / Run = (y2-y1) / (x2 - x1)

y2 = 80 ; y1= 62 ; x2 = 6 ; x1 = 0

m = (80 - 62) / (6 - 0)

m = 18 / 6

m = 3

Intercept, b = value of y when x = 0

(0, 62) ; hence, b = 62

y = 3x + b

y = 3x + 62

3 0
3 years ago
Find the x-intercept of each line defined below and compare their values.
Anettt [7]
X intercept of line a is (-6,0)

x intercept of line b is (1,0)

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3 years ago
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WINSTONCH [101]

Simplify:

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3 years ago
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Determine the maximized area of a rectangle that has a perimeter equal to 56m by creating and solving a quadratic equation. What
sveticcg [70]

Answer:

Area of rectangle = 196\,m^2

Length of rectangle = 14 m

Width of rectangle = 14 m

Step-by-step explanation:

Given:

Perimeter of rectangle is 56 m

To find: the maximized area of a rectangle and the length and width

Solution:

A function y=f(x) has a point of maxima at x=x_0 if f''(x_0)

Let x, y denotes length and width of the rectangle.

Perimeter of rectangle = 2( length + width )

=2(x+y)

Also, perimeter of rectangle is equal to 56 m.

So,

56=2(x+y)\\x+y=28\\y=28-x

Let A denotes area of rectangle.

A = length × width

A=xy\\=x(28-x)\\=28x-x^2

Differentiate with respect to x

\frac{dA}{dx}=28-2x

Put \frac{dA}{dx}=0

28-2x=0\\2x=28\\x=14

Also,

\frac{d^2A}{dx^2}=-2

At x = 14, \frac{d^2A}{dx^2}=-2

So, x = 14 is a point of maxima

So,

y=28-x=28-14=14

Area of rectangle:

A=xy=14(14)=196\,m^2

Length of rectangle = 14 m

Width of rectangle = 14 m

5 0
3 years ago
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