Two different box-filling machines are used to fill cereal boxes on an assembly line. The critical measurement influenced by these machines is the weight of the product in the boxes. Engineers are quite certain that the variance of the weight of product is 1 ounce. Experiments are conducted using both machines with sample sizes of 36 each. The sample averages for machines A and B are 4.5 ounces and 4.7 ounces respectively. Engineers are surprised that the two sample averages for the filling machines are so different. a. Use the CLT to determine the distribution of �$! − �$ ". b. What is �(�$! − �$ " ≥ 0.2)?

Answer:

Explained below.

Step-by-step explanation:

Let X represents the tree heights.

It is provided that X follows a normal distribution with mean μ = 112 inches and standard deviation σ = 10 inches.

(a)

Compute the 22nd percentile of the tree heights as follows:

[tex]P(X<x)=0.22\\\\P(Z<z)=0.22[/tex]

The z-score for the corresponding probability is, z = -0.77.

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\-0.77=\frac{x-112}{10}\\\\x=112-(0.77\times 10)\\\\x=104.3[/tex]

Thus, the 22nd percentile of the tree heights is 104.3 inches.

(b)

Compute the 80th percentile of the tree heights as follows:

[tex]P(X<x)=0.80\\\\P(Z<z)=0.80[/tex]

The z-score for the corresponding probability is, z = 0.84.

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\0.84=\frac{x-112}{10}\\\\x=112+(0.84\times 10)\\\\x=120.4[/tex]

Thus, the 80th percentile of the tree heights is 120.4 inches.

(c)

Compute the first quartile of the tree heights as follows:

[tex]P(X<x)=0.25\\\\P(Z<z)=0.25[/tex]

The z-score for the corresponding probability is, z = -0.67.

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\-0.67=\frac{x-112}{10}\\\\x=112-(0.67\times 10)\\\\x=113.3[/tex]

Thus, the first quartile of the tree heights is 113.3 inches.

(d)

The tallest 1% of the trees, i.e. P (X > x) = 0.01.

That is, P (X < x) = 0.99.

⇒ P (Z < z) = 0.99

The corresponding z-value is, z = 2.33.

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\0.99=\frac{x-112}{10}\\\\x=112+(0.99\times 10)\\\\x=121.9[/tex]

Thus, the tallest 1% of the trees are more than 121.9 inches tall.

Step-by-step explanation:

Perimeter of a rectangle = 2(L+W)

L is the length of the rectangle:

W is the width of the rectangle.

Given

Perimeter = 214feet

If the length is 41 ft longer than the width, then L = 41+W

Substitute L = 41+W into the formula:

P = 2(L+W)

214 = 2(41+W+W)

214 = 2(41+2W)

214 = 82+4W

4W = 214-82

4W = 132

W = 132/4

W = 33 feet

Since L = 41+W

L = 41+33

L = 74 feet

Hence the dimension of the field is 74ft by 33ft

The width of the playing field is 33feet

Convert any mixed numbers to fractions.

Then you get your initial equation

Applying the fractions formula for subtraction

Simplifying 72/16, the answer is

4 1/2

Answer:

B

Step-by-step explanation:

I think its B because the line would be closest to the rest of the dots in the graph. I hope its right!

Answer:

[tex]m=3[/tex]

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug in the 2 coordinates into the slope formula to find slope m:

[tex]m=\frac{5-2}{4-3}[/tex]

[tex]m=\frac{3}{1}[/tex]

[tex]m=3[/tex]

Answer:

Step-by-step explanation:

Select all of the object sets that could be modelled by perpendicular lines.

A perpendicular line is one that divides a 180 degrees line (or a straight line) into two; creating 90 degrees on one hand and 90 degrees on the other.

OPTIONS:

(A) APPLICABLE

Two roads that meet at an intersection can be modelled by perpendicular lines. Use the definition above as a yardstick.

(B) APPLICABLE

The top of the desk to the floor will represent the dividing line while the floor itself will be the 180° line.

(C) NOT APPLICABLE

A tree and its shadow on the ground will only form a right-angled triangle

(D) NOT APPLICABLE

Two stars seen in the sky cannot be modelled by perpendicular lines. They can only be modelled by a straight line; a line which extends from the first star to the other.  

Answer:

-8 < 8

Step-by-step explanation:

-8 is less than 0 so it is definitely less than 8

Hope this helped :)

Answer:

Neither

Step-by-step explanation:

Answer:

9.8

Can i get brainliest please?

Answer:

9.8

Step-by-step explanation:

Hoped that helped :)

Answer:

1000-20

Step-by-step explanation:

Answer:

The first and the third one are correct.

Step-by-step explanation:

Answer: 1 & 3 are proportional relationships

Answer:

965314

Step-by-step explanation:

Please mark me brainlest and hope that help (=

Answer:

The probability that the household has only cell phones and has high-speed Internet is 0.408

Step-by-step explanation:

Let A be the event that represents U.S. households has only cell phones

Let B be the event that represents U.S. households have high-speed Internet.

We are given that 51% of U.S. households has only cell phones

P(A)=0.51

We are given that 70% of the U.S. households have high-speed Internet.

P(B)=0.7

We are given that U.S. households having only cell phones, 80% have high-speed Internet. A U.S household is randomly selected.

P(B|A)=0.8

[tex]\frac{P(A\capB)}{P(A)}=0.8\\P(A\capB)=0.8 \times P(A)\\P(A\capB)=0.8 \times 0.51\\P(A\capB)=0.408[/tex]

Hence the probability that the household has only cell phones and has high-speed Internet is 0.408

Answer:

B and D

Step-by-step explanation:

"Sliding": moving a shape without rotating or flipping it.

The shape still looks exactly the same, just in a different place.

Answer:Step-by-step explanation:

a. Let x = number of months

Amount charged by Francis Lewis Gym = 150 + 10x

Amount charged by Clintonville Gym = 50 + 35x

Set each expression equal to the other to generate an equation to use in finding the number of months for which the cost of membership will be the same at both months

150 + 10x = 50 + 35x

Collect like terms

150 - 50 = -10x + 35x

100 = 25x

Divide both sides by 25

100/25 = x

4 = x

Answer: 4 months

b. Substitute x = 2 into each if the expression of the amount charged by each gym. The one that gives the lowest amount should be the one Mrs. Open should should join.

Amount charged by Francis Lewis Gym = 150 + 10x

= 150 + 10(2)

= 150 + 20

= $170

Amount charged by Clintonville Gym = 50 + 35x

= 50 + 35(2)

= 50 + 70

= $120

She should join the Clintonville Gym if she plans to join a gym for 2 months.

Answer: Clintonville Gym

Answer:

105

Step-by-step explanation:

When finding the perimeter add them together

Answer:

29 units..

Step-by-step explanation:

well i don't know how to insert an image of the answer...but I did it...its (c): 29 units

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: 2.52.5

y-intercept: (0,0)

x y

0 0

1 2.5

丼

Answer:

the anwer is 5*6

Answer: B

Step-by-step explanation:

just took the quiz

A rising unemployment rate affect a society by making it harder for citizens to find jobs.

The term unemployment refers to a situation where a person actively searches for employment but is unable to find work.

As, we know that unemployment means the shortage of jobs for the citizens.

So, rising unemployment rate in society creating trouble for the citizens to find jobs.

Learn more about unemployment here:

https://brainly.com/question/14227610

#SPJ2

Answer:

6 1/6

Step-by-step explanation:

six goes into 42 seven times that leaves you with one number so it can go in six times evenly and that leaves you with 1/6

Answer:

divide by 2 equals 30.5 minus 7 equals to 23,5

Step-by-step explanation:

smaller is 23,5

B is 37.5

Answer:

1.) supplementary  m<1+m<2=180 and m<2+m<3=180

2.) congruent, supplementary

Step-by-step explanation:

the answers are in this order above

Answer:

20

Step-by-step explanation:

its 20 but i.need to explain so 180-110-40=20

Answer:

-1

Step-by-step explanation:

When you make the number line, go to the middle then move left once. Then mark that  " -1 " and you put the dot over that.

It's hard to explain how to write number lines.

Anyways, the problem equals -1 because 6-7 is negative 1. The + is there to confuse you.

Mark brainliest if possible please :)

Answer:

a) -16

b)7

c) -4

d) 9

Step-by-step explanation:

by solving

Answer: -45

Steps: 4.5 × 5 × -2 = -45

Plz mark brainliest:)