2. When an adult is physically active, suppose the amount of water they will consume is normally distributed with an average of 20 ounces of water with a standard deviation of 7 ounces. If 10 adults are physically active, what is the probability that the average water consumed by them is less than 18 ounces? (note that we are working with a sampling distribution in this question). Report to 5 decimal positions

Answers

Answer 1

Using the normal distribution and the central limit theorem, it is found that there is a 0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For the population, the mean and the standard deviation are, respectively, given by [tex]\mu = 20, \sigma = 7[/tex].

For samples of n = 10, the standard error is given by:

[tex]s = \frac{7}{\sqrt{10}} = 2.2136[/tex]

The probability that the average water consumed by them is less than 18 ounces is the p-value of Z when X = 18, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{18 - 20}{2.2136}[/tex]

Z = -0.9.

Z = -0.9 has a p-value of 0.18406.

0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.

To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213


Related Questions

Perimeter of following rectangle mixed number in simplest form 1 1/3 ft 5/8 ft

Answers

Answer: 3 11/12

Step-by-step explanation:

1 1/3 * 2 = 2 2/3

5/8 * 2 = 1 1/4

2 2/3 + 1 1/4 = 3 11/12

I need help...you will be mark brainliest if it's right ty ​

Answers

Answer:

Median: 5

Interquartile range: 4

Have an amazing day!

Please rate and mark brainliest!!

It has been found that 50.3% of U.S. households own stocks and mutual funds. A random sample of 300 heads of households indicated that 171 owned some type of stock. At what level of significance in a two- tailed test would you conclude that this was a significant difference

Answers

Finding the p-value of the test using the z-distribution, as we are working with a proportion, it is found that this was a significant difference for levels of significance of 0.02 and lower.

What are the hypothesis test?

At the null hypothesis, we test if the proportion is of 50.3%, hence:

[tex]H_0: p = 0.503[/tex]

We have a two-tailed test, hence at the alternative hypothesis we test if the proportion is different, that is:

[tex]H_1: p \neq 0.503[/tex]

What is the test statistic?

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.

In this problem, the parameters are:

[tex]n = 300, \overline{p} = \frac{171}{300} = 0.57, p = 0.503[/tex]

Hence:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.57 - 0.503}{\sqrt{\frac{0.503(0.497)}{300}}}[/tex]

[tex]z = 2.32[/tex]

What is the p-value?

Considering a two-tailed test, using a z-distribution calculator, the p-value is of 0.0203. Hence this was a significant difference for levels of significance of 0.02 and lower.

More can be learned about the z-distribution at https://brainly.com/question/26454209

An athlete runs in a straight line along a flat surface. He starts from rest and for 20 seconds accelerate at a constant
rate. In this first 20 seconds he covers a distance of 100m. For the next 10 seconds he runs at a constant speed and
then decelerates at a constant rate for 5 seconds until he stops.
a) What is the total distance that he ran?
[5]
Another athlete runs along the same track, starting from rest and she accelerates at the same rate as her friend. She
however only accelerates for 10 seconds before running at a constant speed.

Answers

Answer:

probably 200

Step-by-step explanation:

or something like that

Think about each of the following. Which of these three triangles is impossible to draw?

Answers

Check by using sum of angles of triangle = 180°

20+45 < 180 so third angle will make it 180 which means it's possible to draw 120+50 = 170< 180 so third angle being 10 will complete the triangle90+100 = 190 > 180 so third angle being (-10) is impossible for the triangle so it can't be possible

Consider the function RX) = 3x + 1 and the graph of the function g(x) shown below.
у
4
6
4
2
X
-6 -4
- 2
12
4
6
-2
4
6
The graph g(x) is the graph of f(x) translated
✓ units
✓, and g(x) =

Answers

Step-by-step explanation:

f(x) goes through the point (0, 1).

g(x) goes through (2, 1) for the same y value.

that means g(x) is f(x) translated 2 units to the right.

but we could also look at the same x value (0).

then g(x) goes through (0, -5).

and that means g(x) is f(x) translated 6 units down.

since it is a line function, shifting it left/right or up/down makes no difference to the shape or position of the new curve itself.

as it looks like you don't have 6 in the drop-down menu, then 2 units (to the right) is the desired correct result.

that means g(x) = f(x-2) = 3(x-2) + 1 = 3x - 6 + 1 = 3x - 5

and that is what the graph is showing us.

the legnth of a rectangle is three times its width. if the length of the perimeter is 64 in, find the length and width

Answers

Answer:

Length and width of rectangle is 24 and 8 inches

Step-by-step explanation:

Given:

Length of rectangle is three times the widthPerimeter of rectangle is 64 Inches

To Find:

Length and Width

Solution:

Let's assume Width of rectangle x inches and length be 3x inches. To calculate the dimensions of The rectangle we will use the formula of Perimeter of rectangle:

Perimeter of rectangle = 2(L + B)

→ 64 = 2(3x + x)

→ 64 = 2(4x)

→ 64/2 = 4x

→ 32 = 4x

→ 32/4 = x

→ 8 = x

Hence,

Length of the rectangle = 3x = 3(8) = 24 inches

Width of the rectangle = x = 8 inches

Answer:

Length = 24 inches

Width = 8 inches

Step-by-step explanation :

As it is given that, the legnth of a rectangle is three times its width and the perimeter is 64 in and we are to find the length and width of the rectangle. So,

Let us assume the width of the rectangle as w inches and therefore, the length will be 3w inches .

Now, According to the Question :

[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{2 (3 x + x )= 64 }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{2 (4x )= 64 }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{8x= 64 }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{ x = \dfrac{64}{8} }}}}[/tex]

[tex]{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 8}} }}} }\: \: \bigstar[/tex]

Therefore,

The width of the rectangle is 8 inches .

Now, We are to find the length of the rectangle:

[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3x }}}}}[/tex]

[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3 \times 8 }}}}}[/tex]

[tex]{\longrightarrow \qquad{ \underline{ \boxed{ \frak{\pmb{Length = 24}}}}}} \: \: \bigstar[/tex]

Therefore,

The length of the rectangle is 24 inches .

Four divided by 1,000 rounded to the nearest whole number

Answers

Answer:

4 ÷ 1,000 = 0.004

Rounding up to 0 as the nearest whole number

The quotient of a number and three is six
What is the number?

Answers

Answer:

the quotient of 18 and 3 is 6

Step-by-step explanation:

do the inverse and get 6x3=18

what is 7 times 3 fiths

Answers

Answer:

4-1.5 or 21/5 or 4.2

Step-by-step explanation:

Multiple: 7 * 3/5 = 7 · 3/1 · 5 = 21/5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(21, 5) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seven multiplied by three fifths = twenty-one fifths.

if you answer this question you will get 30 points

Answers

Answer:

2 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Step-by-step explanation:

1+1 is 2

what is the correct distribution of (2x-8)(3x-6) using the distributive property

Answers

Answer:

  6x² -36x +48

Step-by-step explanation:

The terms in one factor are each multiplied by the terms in the other factor. The resulting partial products are then combined. (This works the same as for numerical "long" multiplication.)

  (2x -8)(3x -6) = 2x(3x -6) -8(3x -6)

  = 6x² -12x -24x +48 . . . . . . . form partial products

  = 6x² -36x +48 . . . . . . . collect terms

Answer:

6x² - 36x + 48

Step-by-step explanation:

(2x-8)*(3x-6) = 2x*3x + 2x* -6 + -8*3x + -8*-6

6x² - 12x - 24x + 48

6x² - 36x + 48 [Answer]

PLEASE RATE!! I hope this helps!!

if you have any questions comment below!!

(I have verified my answer using an online calculator)

Write the given expression in terms of x and y only sin(tan^-1(x)+tan^-1(y)

Answers

Answer:

Step-by-step explanation:

Let a = tan⁻¹(x), so tan(a) = x,

[tex]\sin(a)=\frac{x}{\sqrt{1+x^2}}, \cos(a)=\frac{1}{\sqrt{1+x^2}},[/tex]

Let b = tan⁻¹(y), so tan(b) = y,

[tex]\sin(b)=\frac{y}{\sqrt{1+y^2}}, \cos(b)=\frac{1}{\sqrt{1+y^2}},[/tex]

sin( tan⁻¹(x) +  tan⁻¹(y)) = sin(a + b)

= sin(a) cos(b) + cos(a)sin(b)

= [tex]\frac{x}{\sqrt{1+x^2}}\times\frac{1}{\sqrt{1+y^2}}+ \frac{y}{\sqrt{1+y^2}}\times\frac{1}{\sqrt{1+x^2}}[/tex]

[tex]=\frac{x+y}{\sqrt{(1+x^2)(1+y^2)}}[/tex]

Sonya took out a mortgage of $65,000 at 7% for 25 years. What is the cost of the mortgage?

Answers

The cost of the mortgage is $81250

What are interests?


Interests are percentages of a principal

Given the following parameters

Principal = $65000

Rate = 7% = 0.07
Time = 5 years

Calculate the interest

I = PRT/100
I = 65000*0.07*25
I = 16,250

Determine the cost of the mortgage

Cost of mortgage = Principal + Interest

Cost of mortgage = 65000 + 16250
Cost of mortgage = 81,250

Hence the cost of the mortgage is $81250

Learn more on mortgage here: https://brainly.com/question/22846480

Answer:

$72,823

Step-by-step explanation:

just took test

Find the differential of
f
(
x
,
y
)
=
x
2
+
y
3
at the point
(
2
,
1
)
.

Answers

[tex]f(x,y)=x^2+y^3\implies \left.\cfrac{}{} 2x+3y^2 \right]_{\stackrel{\textit{\small x=2}}{\textit{\small y=1}}}\implies 2(2)+3(1)^2\implies 7[/tex]

Work out the highest common factor (HCF) of 18 and 30

Answers

[tex]18 = 2\times 3 \times 3\\\\30 = 2 \times 3 \times 5\\\\\text{HCF}~ = 2\times 3 = 6[/tex]

what should be the rate of interest to earn an 45000 as interest wale rupees 50000 easy in investment for 6 year​

Answers

Answer:

5

Step-by-step explanation:

Briana has 3/4 pound of rabbit food. She feeds her rabbit 1/12 pound each day. How many days can Briana feed her rabbit with the food she has?

Answers

The answer is 9 days. I have attached my working with it. Hope this helps!
Answer: 3 pounds

Hope this helps you!

What is the area?
2 yd
8 yd
5 yd

Answers

Answer:

28

Step-by-step explanation:

I assume the polygon is a trapezoid with parallel bases of 2 yd and 5 yd, and an altitude of 8 yd.

area of trapezoid = (base1 + base2)h/2

area = (2 yd + 5 yd)(8 yd)/2

area = 28 yd²

A parabola can be drawn given a focus of (1, -7) and a directrix of y = 1. Write the
equation of the parabola in any form.

Answers

Answer:

Step-by-step explanation:

focus (1 , -7)  ⇒ a = 1  & b = -7

y = 1 ⇒ c = 1

Equation of parabola :

(x - a)² + (y - b)² = (y - c)²

(X - 1)² + (y + 7)² = (y - 1)²

Now, expand.

x² - 2x + 1 + y² + 2*7*y + 7² = y² - 2*y*1 + 1

x² - 2x + 1 + y² - 14y + 49 = y² - 2y +1

x² - 2x + 1 + y² - 14y +  49  - y² + 2y - 1 = 0

x² - 2x  + y² - y²   - 14y + 2y   + 1 + 49 - 1 = 0

x² - 2x  - 12y + 49 = 0

Please help Math-correct answers only!!

Have number with correct answers/letters!

Answers

I'll do the first three questions to get you started.

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

Question 1

x = horizontal component of the triangle

cos(angle) = adjacent/hypotenuse

cos(theta) = horizontal/hypotenuse

cos(40) = x/30

x = 30*cos(40)

x = 22.98133329 approximately

This is the horizontal force applies to the suitcase.

Work = force*displacement

Work =  22.98133329*120

Work = 2,757.7599948

Work = 2,758

Answer:   2,758 Nm (choice B)

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

Question 2

Add the drone's relative air velocity and the wind velocity vectors.

v+w = (13i + 3j) + (-7i - 2j)

v+w = (13i-7i) + (3j-2j)

v+w = 6i + j

Answer:  6i + j  (choice B)

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

Question 3

Check out the diagram below. Focus on the smaller triangle. Notice the placement of angle theta.

sin(theta) = opposite/hypotenuse

sin(40) = x/200

x = 200*sin(40)

x = 128.557521937308

x = 128.558

Answer:  128.558 pounds (choice A)

3
0.33 points
Suppose you form 5-letter strings from the letters C,O, M, P, U, T, I, N, and G. What are the number of permutations as a ratio of factorials?
type your answer...

Answers

Using the permutation formula, it is found that it's number as a ratio of factorials is given by:

[tex]N = \frac{9!}{4!}[/tex]

The order in which the letters are chosen is important, hence the permutation formula is used to solve this question.

What is the permutation formula?

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, five letters will be chosen from a set of nine, hence:

[tex]N = P_{(9,5)} = \frac{9!}{(9-5)!} = \frac{9!}{4!}[/tex]

More can be learned about the permutation formula at https://brainly.com/question/25925367

Which angle is an x-intercept for the function y = cos(1)
A.0
B.2
C. £
D. 2£

Answers

Answer: C. [tex]\pi[/tex]

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

Explanation:

The x intercept always occurs when y = 0.

Use the unit circle to determine that [tex]\cos(\theta) = 0[/tex] when [tex]\theta = \frac{\pi}{2} \text{ and } \theta = \frac{3\pi}{2}[/tex]

So if [tex]x = \pi[/tex], then we have

[tex]y = \cos\left(\frac{1}{2}x\right)\\\\y = \cos\left(\frac{x}{2}\right)\\\\y = \cos\left(\frac{\pi}{2}\right)\\\\y = 0\\\\[/tex]

which shows us that [tex](\pi, 0)[/tex] is the location of one of the infinitely many x intercepts for this function.

what does Y=
what does z=

Answers

Answer:

Hope the picture will help you

Pleade god help me find someone to help me thank you

Answers

Answer:

yw

Step-by-step explanation:

makin a chart :)

Which method do you prefer when comparing numbers written in scientific notation? Explain why you prefer this method using examples. PLS HURRY

Answers

Answer:

If two numbers have the same exponent for 10, then compare the decimal numbers to determine the greater number. Sometimes you may have to compare two numbers, but only one of them is in scientific notation. In that case, convert the number that is not in scientific notation into scientific notation first. Then, compare the two numbers. Example 1 : Compare 5.62 x 10 6 and 7.39 x 10 5.

Step-by-step explanation:

The general form in scientific notation is

z.z ×10^z

where z is integer

So while comaparing

We usually compare z.z rounded to similar significant numbers .

In rest case

we use power of 10 ,the number which has higher that's bigger.

Example

1.27×10⁴1.24×10⁴

First one is bigger

A runner is preparing for a marathon that is divided into 5 sections of equal distance. The Marathon is 42.195 km long. How long is each section of the marathon?
A. 210.975
B. 21.0975
C. 8.439
D. 0.8439

Answers

Answer:

8.439

Step-by-step explanation:

Since the marathon is divided on 5 EQUAL sections, and it is 42.195 km long, you only need to divide the length of the marathon by 5.

​Triangle A′B′C′​ is a dilation of ​triangle ABC​ .
What is the scale factor?
Enter your answer in the box.

Answers

Answer:

1/2

Step-by-step explanation:

The scale factor is 1/2 because each side length of [tex]\triangle{A'B'C'}[/tex] is 1/2 of the length of the side lengths of [tex]\triangle{ABC}[/tex].

Hope this helps :)

Answer:

1/2

Step-by-step explanation:

took the test

26.95 divided by -5 1/2. can someone show me how to do it please?

Answers

Answer:

-4.9

Step-by-step explanation:

Since the number 26.95 has two decimal places, it can be turned into a whole number with a denominator having two zeroes; 100

        2695

         100

Then change -5 1/2 into an improper fraction; = -5 × 2 + 1

                                                                                    2

                                           = -11/2

2695 ÷ ( -11 )

 100         2

  Reciprocate (put denominator as numerator and vice-versa ) the equation after the ÷ sign. After doing so, the ÷ sign changes to × sign.

Hence:   2695 × ( 2 )

                 100      -11

Then, cross multiply.

2695 ÷ ( -11 )   =  -245

          100 ÷ 2              50

     -245 ÷ 50

         = -4.9

 

Answer: its -4.9

Step-by-step explanation:

What is the volume of a rectangular prism that is 4 ft. by 12 ft. by 6 ft.? Question 21 options: 324 ft.³ 205 ft.³ 288 ft.³ 315 ft.³

Answers

Answer:

288 ft³

Step-by-step explanation:

The formula to find the volume of a rectangular prism is :

Volume = length × width × height

Let us find it now.

Volume = 4 ft × 12 ft × 6 ft

Volume = 48 ft² × 6 ft

Volume = 288 ft³

Other Questions
What's the area of this figure? brain boggling boggle help pls:) Richard and Teo have a combinedage of 23. Richard is 2 years older than twice Teo's age. How old are Richard andTeo? How long is 10% of a 24-hour day? What powers does the supreme court have in choosing cases Which is the best explanation for how earthquakes cause tsunamis?. A hockey puck of mass 150 g is sliding south along the ice and slows at a rate of 1.2m/s2. What is the net force acting on the puck? Escribe, en un prrafo de entre 5 y 10 lneas, las diferencias que encontraste al expresarte de manera oral y escrita. please answer the worksheet attached below Please help me on all of these problems i am confused how they correlate in the four graphs below, determine what transformation was used to transform ABC to ABC. then, for each one, write the correct description of the transformation along with the algebraic notation Which marketing tactic runs counter to the practice of market segmentation?undifferentiated marketingtargeted marketingmarketing campaigndemographic marketing What have you learned from geography give 2-3 sentences? Evaluate the expression 2bc for b = 1.5 and c = 5. Find the solution of the system of equations shown on the graph Zoe has a circular shaped rug on her bedroom floor. The diameter of the rug is 8 feet. What is the circumference of the rug?6.28 feet12.56 feet25.12 feet50.24 feet Which type of wave needs a medium to travel? (1 point)Olight waves, because they travel by oscillating moleculesO light waves, because they travel by oscillating electromagnetic fieldsO sound waves, because they travel by oscillating moleculesO sound waves, because they travel by oscillating electromagnetic fields Which of the following are included in the five themes of geography?Check all that apply.A. Physical goggraphyO B. LocationC. Human-environmental interactionD. Cartography Myra has been at a party for two hours and had four drinks. Suddenly, she needs to leave the party sooner than expected. Her friends are concerned about her driving, but Mayra says that she will grab some coffee on the way home. What is the BEST response to Mayra?A. She is not safe to drive, and coffee will not help.B. The coffee will probably make her alert enough to drive.C. She could safely leave the party if she waited another half hour.D. Mayra is an adult and can make her own decisions about driving. 1. What has influenced Garcia's work?2. What point does Garcia make about Act I? How does thisinfluence the story created?3. What makes characters complex? What are some of the waysGarcia creates great characters?4. Who is the unlikeable character for Garcia? How does heconnect with them?5. A section of the movie is titled, "Fighting the Beast of CreativeInsecurity." Explain what Garcia says the beast is and howyou fight it.