Suppose the average age of family members is 34 with a standard deviation of 4. if 100 members of the community decided to have a summer outing bonding and relaxation, find the probability that the average of these members is less than 35?

Answers

Answer 1

Using the normal distribution, it is found that there is a 0.9938 = 99.38% probability that the average of these members is less than 35.

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].

In this problem, we have that the parameters are given as follows:

[tex]\mu = 34, \sigma = 4, n = 100, s = \frac{4}{\sqrt{100}} = 0.4[/tex].

The probability that the average of these members is less than 35 is the p-value of Z when X = 35, hence:

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

By the Central Limit Theorem

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

[tex]Z = \frac{35 - 34}{0.4}[/tex]

Z = 2.5

Z = 2.5 has a p-value of 0.9938.

0.9938 = 99.38% probability that the average of these members is less than 35.

More can be learned about the normal distribution at https://brainly.com/question/24663213

#SPJ1


Related Questions

O
O
O
-54-3 -2 -1 0 1 2 3 4 5 6 7
8
-5-4
-3 -2 -1 0 1 2 3 4 5 6 7 8
++
-5 -4
-3 -2 -1
0 1
2
3 4 5 6 7
8
+
-5 -4
-3 -2 -1 0 1
2
3
5
6
7
C
C
4
8
9 10 11 12 13
9 10 11 12 13
9 10 11 12 13
9 10 11 12 13

Answers

Step-by-step explanation:

separate the question into two inequalities then solve individually to derive at an answer then merge the two answers as one.

remember that < or > are open sets while <= or >= are closed set.

Rewrite the expression using the distributive property and a common factor.

27x+24x
0.5n+2.5

Answers

Answer:

x(27 +24)  or  3x(9 +8)0.5(n +5)  or  2.5(n/5 +1)

Step-by-step explanation:

The distributive property of multiplication over addition tells us that the product of a value and a sum will be the same as the sum of products of the value and the sum's addends. This property can be used to add or remove parentheses from an arithmetic expression.

  a(b +c) = ab +ac . . . . expression of the distributive property

__

When applying the distributive property to a sum, the first step is to look for a factor common to the terms of the sum. That factor need not be the greatest common factor, though it is often useful if it is.

Below, we have written each expression using two different common factors.

a)

  27x +24x = x(27 +24) = 3x(9 +8)

__

b)

  0.5n +2.5 = 0.5(n +5) = 2.5(n/5 +1)

_____

Additional comment

Finding a common factor can make use of knowledge of multiplication tables, rules of exponents, and identities involving various functions used in algebraic expressions. It is sometimes useful to list the prime factors of each of the terms as an aid to finding a common one. Where fractions are involved, it is sometimes helpful to express them all using a common denominator.

The Euclidean Algorithm can also be useful for finding common factors.

According to the histogram shown, how many hostel rooms are there?

Answers

Answer:

10

Step-by-step explanation:

look at the y axis for the answer to a question like this

Answer:

There are 25 hostel rooms.

Step-by-step explanation:

We simply need to add up the height of each bar.

3+5+8+6+2+1=25 hostel rooms

Determine x to two decimal places.
*PICTURE ATTACHED*
*TRIGONOMETRY*​

Answers

This rule is applied to triangles to determine the unknown sides and angles. The value of x from the diagram is 11.78m

Trigonometry rule

This rule is applied to triangles to determine the unknown sides and angles.

Given the following parameter

Opposite = 5m

Adjacent = x

angle = 23 degrees

According to the theorem of tangents

tan23 = opposite/adjacent

tan23 = 5/x
x = 5/tan23

x = 11.78m

Hence the value of x from the diagram is 11.78m

Learn more on trig identity here: https://brainly.com/question/7331447

#SPJ1

Evaluate each function.
14) g(x)= 3x² - 1; Find g(-3)

Answers

[tex]g(x) =3x^2 -1\\\\g(-3)=3(-3)^2 -1 \\ \\~~~~~~~~~=3(9) -1 \\\\~~~~~~~~~=27-1\\\\~~~~~~~~~=26[/tex]

Answer:

g(26)

Step-by-step explanation:

 

substitute -3 for x.

g(x)=3[tex]x^{2}[/tex]-1

[tex]g(-3)=3(-3)^{2} -1\\g(-3)= 3(9)-1\\g(-3)= 27-1\\g(-3)=26[/tex]

(-14,-13), (-7,-7)

Can anyone help me solve this - algebra

Answers

Answer: y=6/7x-1

Step-by-step explanation:

I am assuming you want a line formula in y=mx+b

slope (y2-y1)/(x2-x1) = -7+13/-7+14 = 6/7

y+7=6/7(x+7)

y+7 = 6/7x+6

y=6/7x-1

What expression is equivalent to the given expression?

Answers

The expression which is equivalent to the given expression is     [tex]\frac{27 m^{5}}{n}[/tex]

Evaluating indices

From the question, we are to determine the expression which is equivalent to the given expression

The given expression is

[tex]\frac{(3m^{2}n)^{3} }{mn^{4} }[/tex]

Clearing the brackets, we get

[tex]\frac{3^{3} m^{2(3)}n^{3} }{mn^{4} }[/tex]

Simplifying, we get

[tex]\frac{27 m^{6}n^{3} }{mn^{4} }[/tex]

Then,

[tex]27 m^{6-1}n^{3-4}[/tex]

[tex]27 m^{5}n^{-1}[/tex]

= [tex]\frac{27 m^{5}}{n}[/tex]

Hence, the expression which is equivalent to the given expression is     [tex]\frac{27 m^{5}}{n}[/tex]

Learn more on Simplifying indices here: https://brainly.com/question/14026660

#SPJ1

Solve the system using substitution.
y=-x-2,3x+3y=6

Answers

Step-by-step explanation:

x = -2-y

3(-2-y) +3y =6

-6-3y +3y=6

у=0

O=-x-2

х=-2

Which fraction names the shaded part of the set?

Answers

Answer:

Hello! Your answer is 1/2

Step-by-step explanation:

there are six cubes and three of them are shaded. That is half of the parallelograms.

So 1/4 wouldn't make sense because there are three shaded out of six.

1/6 doesn't make sense because since there is six in total for it to be 1/6 there needs to be 1 shaded out of six.

And finally 1/3 doesn't make sense because 1/3 would have to be two out of six shaded.

Have a wonderful day/night/afternoon and good luck my friend!

Okay I just got here I got the truck so I don’t have time for it but I’ll be home safe 1/2

(06.03 HC)

Solve the following system of equations. Show all work and solutions.

y = 3x2 + 6x + 4
y = −3x2 + 4

Answers

By solving the two quadratic equations we found the values (0,-1).

What is a quadratic equation?

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given equations are;-

y = 3x² + 6x + 4y = -3x² + 4

The two equations are solved by equating them and finding the value of x.

3x² + 6x + 4 = -3x² + 4

6x² + 6x = 0

6x ( x+1 ) = 0

6x  = 0 so x = 0

( x+1 ) = 0 so x = -1

Therefore solving the two quadratic equations we found the values (0,-1).

To know more about quadratic equations follow

https://brainly.com/question/1214333

#SPJ1

please help!! What is the most precise classification for the quadrilateral shown in the graph below?

Answers

Parallelogram is the most precise classification for the quadrilateral shown in the graph below.

What is a Parallelogram?

This is a quadrilateral which has two pairs of parallel sides and the area is usually measured using base × height.

The opposite sides and angles are equal which is why parallelogram was chosen as the most appropriate choice.

Read more about Parallelogram here https://brainly.com/question/970600

#SPJ1

Jada fills the bathtub before taking a bath and then allows the water to drain when she is done. The graph below models the number of gallons of water, y, in the bathtub over time, t, in minutes.

On a graph, the graph increases, remains constant, and then decreases.

Is the number of gallons of water in the bathtub a function of time?

Answers

The number of gallons of water in the bathtub is a function of time. Therefore, it is true.

How to illustrate the graph?

The graph shows a curve that lets you find the number of gallons of water given any value of t betweeh 0 and 30 plus.

Hence, the number of gallons of time indeed is a function of time, in the interval shown by the graph.

The answer is true, because each t value is paired with exactly one number of gallons".

Learn more about graph on:

https://brainly.com/question/19040584

#SPJ1

Answer:

A

Step-by-step explanation:

The triangles below are similar. Triangle Y X Z. Side Y X is 6 centimeters, X Z is 7 centimeters, and Z Y is 3 centimeters. Triangle A B C. Side A C is 14 centimeters, A B is 12 centimeters, and B C is 6 centimeters. Which similarity statement expresses the relationship between the two triangles? Triangle Z Y X is similar to triangle C A B Triangle Z Y X is similar to triangle A C B Triangle Z Y X is similar to triangle C B A Triangle Z Y X is similar to triangle A B C Mark this and return

Answers

Answer:

  (c)  Triangle Z Y X is similar to triangle C B A

Step-by-step explanation:

Triangles are similar when corresponding sides have the same ratio. Corresponding sides will have corresponding end point vertices. The similarity statement lists corresponding vertices in the same order.

__

corresponding sides

The side lengths, smallest to largest, for the two triangles are ...

3 cm -- ZY6 cm -- YX7 cm -- XZ

And for the other triangle, ...

6 cm -- BC12 cm -- AB14 cm -- ACcorresponding vertices

The points joining the each side to the next one longer, in order for the two triangles, are ...

  Y, X, Z  and  B, A, C

The vertices corresponding to ZYX in the same order are CBA.

  triangle ZYX is similar to triangle CBA

Answer:

The answer is C

Step-by-step explanation:

What is the relationship between the number of sides a regular polygon has and the number of lines of symmetry that can be found on it?
There are always more lines of symmetry than sides.
They are same value.
There are always more sides than lines of symmetry.
There is no relationship.

Answers

The number of sides equals the number of the line of symmetry. Then the correct option is B.

What is a polygon?

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The relationship between the number of sides a regular polygon has and the number of lines of symmetry will be

In a regular polygon, the amount of symmetry lines is equal to the total of sides.

Then the correct option is B.

More about the polygon link is given below.

https://brainly.com/question/17756657

#SPJ1

Answer:

B They are the same value!

Step-by-step explanation:

Why? Well go look in your lesson although because i got this correct i forgot ago and yeah (TRUST++)

Dan invests £8200 into his bank account.
He receives 2% per year compound interest.
How much will Dan have after 7 years?
Give your answer to the nearest penny where appropriate.

Answers

Answer:  £ 3675.79

Step-by-step explanation:

A = P(1 + r)^t

A = final amount = x

P = initial principal balance = 3200

r = interest rate = 0.02

t = number of years elapsed = 7

x = 3200(1.02)^7

x = 3200 * 1.14868567

x = 3675.79414

x = 3675.79

martina must choose a number between 49 and 95 that is multiple of 2,8 and 10. write all the numbers that she could choose.

Answers

Answer:

80

Step-by-step explanation:

10 limits it to 50, 60, 70, 80, and 90

2 eliminates none since 50=25, 60=30, 70=35, 80=40 and 90=45

8 divided by each number only leaves one option of 80. (80/8= 10) (80/10=8) (80/2=40)

Help please and thank you !! ill give brainle and 20 points !

Answers

Answer:

G 33%

Step-by-step explanation:

17/52 = 0.32692307692

0.32692307692 is about 33 %

Have a nice day! :)

If the quadratic equation has two rational roots,then the discriminant is_____and a perfect square

Answers

Answer:

Real and unequal

Answer:

The quadratic has two equal roots like d if it is perfect square and we may write: (x − d) 2 = x 2 − 2 d x + d 2 Then: Δ = 4 d 2 − 4 d 2 = 0 That is the discriminant is zero when the quadratic is perfect square.

Step-by-step explanation:

6 A cube has a surface area of 54 mm². The length of its sides is: A 3 mm B 4 mm C 5
mm D 6 mm E 7 mm

Answers

Answer:

A

Step-by-step explanation:

A cube has 6 square faces

given surface area = 54 mm² , then

area of one face = 54 mm² ÷ 6 = 9 mm²

the area (A) of a square is calculated as

A = s² ( s is the side length ) , so

s² = 9 ( take square root of both sides )

s = [tex]\sqrt{9}[/tex] = 3 mm

What is the length of segment BC?

Answers

Answer:

[tex]BC=x=(13;+\infty)[/tex]

Step-by-step explanation:

Existence of Triangle            

[tex]x-(2x-24) < x-2 < x+(2x-24)\\[/tex]

                   [tex]13 < x > 11[/tex]

  [tex]x=(13;+\infty)[/tex]

HELP PLEASE !!!!!!!!!!!

Answers

Answer:

I think A sorry if wrong

Step-by-step explanation:

have a good day

In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:

Answers

The slope of the graph is 745 and the y-intercept of the graph is 500

Missing part of the question

The following three points are from the graph: (2, 1990) (5, 4225) (9, 7205)

Find the slope and y-intercept

How to determine the slope?

The points are given as:

(2, 1990) (5, 4225) (9, 7205)

The slope is calculated using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m = (4225 - 1990)/(5 - 2)

Evaluate

m = 745

Hence, the slope of the graph is 745

How to determine the y-intercept?

In (a), we have

m = 745

To calculate the y-intercept, we use the following points

(x1 , y1) = (0,y)

Recall that:

m = (y2 - y1)/(x2 - x1)

So, we have:

745 = (4225 - y)/(5 - 0)

Evaluate the difference

745 = (4225 - y)/(5)

Multiply both sides by 5

3725 = 4225 - y

Solve for y

y = 500

Hence, the y-intercept of the graph is 500

Read more about linear functions at:

https://brainly.com/question/4025726

#SPJ1



Glen Cove has a population of 7,200, which is decreasing at a
rate of 80 people per year. Locust Valley has a population of
5,000 and is gaining 120 people per year. In how many years
will the populations of Glen Cove and Locust Valley be the same?


Please help!!

Answers

Answer:

11 years

Step-by-step explanation:

7200  -  80x  =  5000  +  120x
-5000 + 80x    -5000 + 80x
           2200 = 200x
                  11 = x

Please help on this only if u know

Answers

Answer:

Option D --->  y=5x

Step-by-step explanation:

When a line is directly proportional it means it crosses the origin so has a y- and x-intercept of 0.

So if we use the format y=mx+c, it will work but our c value will be 0 as I explained above .

To work out the gradient we simply take 2 points (0,0) and (1,5)) on the graph and use the gradient formula :

m = change in y ÷ change in x

m = 5÷1

m = 5

Therefore our direct proportion equation will be y=5x

Hope this helped and have a good day

What is the value of x in the equation shown Below?2(x+4)-4x=10x-4

Answers

Answer: 1

Step-by-step explanation:

Solve for x

3x-5=-x+3

Answers

Answer:

(3x - 5 = -x + 3) x = 2

Step-by-step explanation:

3x - 5 = -x + 3

3x = -x + (3 +5)

3x=-x + 8

(3x + x ) = 8

4x = 8

4/8 =2

x = 2

Daniel runs 40/5 miles in 124/₁ minutes. What is the unit rate in terms of miles per minute? What the answer:

Answers

Using the given information, the unit rate is 0.0645 miles/minute

Calculating rate

From the question, we are to determine the unit rate

From the given information,

Daniel runs 40/5 miles in 124 minutes

That is,

Distance = 40/5 miles = 8 miles  

Time = 124 minutes

Using the formula,

Rate = Distance / Time

Rate = 8 miles / 124 minutes

Rate = 0.0645 miles/minute

Hence, the unit rate is 0.0645 miles/minute

Learn more on Calculating rate here: https://brainly.com/question/1090517

#SPJ1

The unit rate is 0.0645 miles/minute

We have calculated the rate

From the question, we are to determine the unit rate

From the given information,

Daniel runs 40/5 miles in 124 minutes

Distance = 40/5 miles

Distance = 8 miles  

Time = 124 minutes

What is the formula of rate?

Rate = Distance / Time

Rate = 8 miles / 124 minutes

Rate = 0.0645 miles/minute

Hence, the unit rate is 0.0645 miles/minute

To learn more about calculating rates visit:

brainly.com/question/1090517

#SPJ1

Cheryl has a horse and cow ranch that contains 100 animals. The value of each horse is $500 and the value of each cow is $200. If the total value of the 100 animals is $31,000, how many horses and cows does Cheryl have on her ranch?​

Answers

The number of the cows is 63 and the number of the horses is 37.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

Cheryl has a horse and cow ranch that contains 100 animals. The value of each horse is $500 The value of each cow is $200. If the total value of the 100 animals is $31,000.

The number of horses and cows will be calculated by forming the expression from the given data in the question. So the two expressions are as follows.

h  +  c  = 100

500h  +  200c  =  31000

Solving the above two equations by substitution method:-

h  =  100  -  c

Put the value of h in the second equation:-

500 ( 100 - c ) + 200c = 31000

50000 - 500c  + 200c =  31000

50000 - 300c  =  31000

50000 - 31000 = 300c

c  =  19000 / 300

c = 63

Put the value of c in the first equation we will get the number of the horses.

h  + c  =  100

h  +  63  =  100

h  =  100-67  =  37

Therefore the number of the cows is 63 and the number of the horses is 37.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ1

Find the value of x. Show each step.

0.15x+(0.15-5-x)*0.2=0.1

Answers

Answer:

-21.4

Step-by-step explanation:

0.15x + 0.2(0.15-5-x) = 0.1

0.15x + 0.03 - 1 - 0.2x = 0.1

0.15x - 0.2x = 0.1 -0.03 + 1

-0.05x = 1.07

0.05x = -1.07

x = -21.4

What is the amplitude of the graph below

Answers

The amplitude is 3

for a sine graph, the amplitude is the distance up or down from the midway point. The equation to find the amplitude is (max-min) / 2.

(3 - (-3)) / 2 = 3

Other Questions
Solve for hh - 3h - 8 = 14H=? Which one of following is not example of governance that developed by customs The diameter of a semicircle is 8 kilometres. What is the semicircle's perimeter? please help will mark brainliest If you have 3 moles of gas at a pressure of 2.5 atmospheres and a volume of 8 liters, what is the temperature? Pay attention to the unit of pressure used. A.) 81.27 KB.) 0.81 KC.) 57.86 KD.) 25 K What challenges did the aztecs environment pose for farmers?. what is the specific heat capacity of propan-1-ol What is the missing term?+1 4x -33x 12x?4x - 3 three consecutive integers such that the smallest and three times the largest is 330 . what is the smallest integer? Which sentence needs a comma before the coordinating conjunction?Group of answer choicesLin drove all the way across the country to visit his aunt, uncle, cousins, and grandparents.We need butter and eggs and milk and tea from the store.Addie can only stand so much chocolate before she gets sick.Ian didn't take his math test yesterday but he plans to take it today.I need a answer ASAP AGAIN what is the percent increase of 42 from 30? Does a nation have the moral right to impose its political values on another nation by intruding on the sovereignty of that nation? Use examples from World War 2 and concept language to support your answer. The layer of the uterine wall that is shed during menstruation is the:. Drag each tile to the correct boxAmange the organisms according to their positions in the food web, starting with the autotraphs. Car A is traveling with a constant velocity of 18 [m/s]. Car B speeds up from 0 [m/s] to 10 [m/s] in 4 seconds. Which car has a greater acceleration? A website advertises 85 video games for $1969. How much would 160 video games cost at the same unitprice? In the group of three sentences, choose one sentence which tells a main idea and two sentences which state supporting details for the main idea. Type MI beside the main idea sentence and D beside each detail sentence.1. Churro and merino sheep are used for different purposes.2. Churro sheep provided such delicious mutton for eating.3. Merino sheep provided fine wool. which type of sensory impairment is appropriate for a 4-year-old child who has difficulty processing... A man stands on his balcony, 140 feet above the ground. He looks at the ground, with his sight line forming an angle of75 with the building, and sees a bus stop. The function d=140 sec 0 models the distance from the man to any object givenhis angle of sight 0. How far is the bus stop from the man? Round your answer to the nearest foot. [tex]-6 + 3x - 9x^{2}=-16[/tex]