Answer:
0.0802 = 8.02% probability that the sample mean would differ from the population mean by more than 2.2 millimeters
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Their current steel bolts have a mean diameter of 148 millimeters, and a standard deviation of 7 millimeters.
This means that [tex]\mu = 148, \sigma = 7[/tex]
Sample of 31:
This means that [tex]n = 31, s = \frac{7}{\sqrt{31}}[/tex]
What is the probability that the sample mean would differ from the population mean by more than 2.2 millimeters?
Less than 148 - 2.2 = 145.8 or more than 148+2.2 = 150.2. Due to the simmetry of the normal distribution, these probabilities are the same, which means that we find one and multiply by 2.
Probability of being less than 145.8:
The pvalue of Z when X = 145.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{145.8 - 148}{\frac{7}{\sqrt{31}}}[/tex]
[tex]Z = -1.75[/tex]
[tex]Z = -1.75[/tex] has a pvalue of 0.0401
2*0.0401 = 0.0802
0.0802 = 8.02% probability that the sample mean would differ from the population mean by more than 2.2 millimeters
tonya earned $5.00 she put half of the money into savings and kept the rest to spend.she bought a toy for $2.00.how much spending money dose tonya have left?
Answer:
50 cents
Step-by-step explanation:
half of 5.00$ is 2.50$
I need help what is the answer
9514 1404 393
Answer:
6π
Step-by-step explanation:
The circumference of a circle is given by the formula ...
C = πd
The arc length of a semi-circle is half that, so is ...
arc length = (1/2)πd = 1/2·π·12 = 6π . . . units
for a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is R(x)=-0.5(×-110)^2+6,050. the maximum capacity of the company is 160 items.
Answer :
Step-by-step explaation:
c(80) =40x80 +150 =3350 üretim için 80 parçanın maliyeti
satış için ise : R(80) 0.5(80-110)^2+6,050 = 456
3350-456=2983.95 kar ederler
Please help me fast i need help please
Answer:
30
Step-by-step explanation:
because I find the lcm for each number
A group of 540 students are required to take a test. Of these,
495 actually take the test, and 45 are absent that day.
(i) Write down the ratio of the number of students who take the test
to the number of students who are absent. Simplify this ratio as far
as possible.
What is 6^4written in expanded form?
4+4+4+4+4+4
4.4.4.4.4.4
6+6+6+6
6.6.6.6
Answer:
6 · 6 · 6 · 6
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
This is because the 4 is an exponent or a power.
This makes the 6 in this case multiply itself 4 times.
HOPE THIS HELPS
show proof and show work for brainliest
Answer:
-2(4-1)
Step-by-step explanation:
Do parentheses first because of PEMDAS. That means 4-1 equals 3. Then take -2 and times it by the 3 to get -6.
Answer:
The answer would be -2(4-1)
Step-by-step explanation:
-2 multiplied by 4 is -8
-2 multiplied by -1 is 2
you then add -8 and 2 which equals -6
Find the work W done by a force of 3 pounds acting in the direction 60° to the horizontal in moving an object 4ft (0,0) to (4,0)
Answer:
[tex]\frac{3}{2}i + \frac{3\sqrt{3} }{2}[/tex]j
Step-by-step explanation:
The work done by the force in moving the object is 10 ft-lb.
What is force?Force is an influence or interaction that can change the motion or shape of an object with mass.
It can be described as a push or a pull that has both magnitude and direction.
Force is equal to the product of the mass of the object and its acceleration.
Given,
F = 3 p
d = 4 ft
The work formula:
W = F x d
W = 4 p x cos 60° x 5 ft
= 10 ft lb.
Hence, the work done by the force in moving the object is 10 ft-lb.
Learn more about force click;
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Please answer number 7 I’ll give brainliest
Answer:
A $48.15
Step-by-step explanation:
7% of $45 is 3.15 so you would add 3.15 to $45 to get $48.15
Find the distance between the two points rounding to the nearest tenth (if necessary).
(8,-3) and (4,6)
Answer:
9.8
Step-by-step explanation:
x1 = 8 x2 = 4 y1 = -3 y2 = 6
[tex]\sqrt{(x2 - x1)^{2}+(y2 - y1)^{2}[/tex]
[tex]\sqrt{(4 - 8)^{2}+(6 - -3)^{2}[/tex]
= 9.8488
= 9.8
A football is kicked into the air. The height of the football can be modeled by the equation
h = -16x^2 + 16x, where h is the height reached by the ball after x seconds. When does the
ball touch the ground?
Answer:
x = 0 and x = 1
Step-by-step explanation:
Given that,
A football is kicked into the air. The height of the football can be modeled by the equation :
[tex]h = -16x^2 + 16x[/tex]
Where
h is the height reached by the ball after x seconds
When it touches the ground, h = 0
So,
[tex]-16x^2 + 16x=0\\\\16x(-x+1)=0\\\\x=0\ and\ x=1[/tex]
So, it will touch the ground at x = 0 and x = 1 seconds.
The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results? What is the estimate of the mean proportion of failures for these instructors?
INSTRUCTOR NUMBER OF FAILURES
Prof. A 13
Prof. B 0
Prof. C 11
Prof. D 16
Answer:
D. 16
Step-by-step explanation:
A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results:
MACHINE MEASUREMENTS
#1 17 15 15 17
#2 16 25 18 25
#3 23 24 23 22
Auto racing is a sport enjoyed by many people. In each race, there may be up to 25 cars on the racetrack. Which of the following is NOT an example of a quantitative variable you might use to describe a car in a race?
the brand of car
the number of tires used
the number of laps completed
the average speed (in mpg)
Answer:
A is correct i assume
Step-by-step explanation:
Answer:
The correct answer is A
Step-by-step explanation:
The person above me assumed correctly lol
0.36(18)+0.04x=0.12(24+x)
Answer:
x = 45
Step-by-step explanation:
0.36(18) + 0.04x = 0.12(24 + x)
6.48 + 0.04x = 2.88 + 0.12x
0.04x - 0.12x = 2.88 - 6.48
-0.08x = -3.6
0.08x = 3.6
x = 3.6/0.08
x = 45
helppppppppp i m on my test
On the top of a hill stands a tower that is 50 feet tall. From a point that is on the same
level as the base of the hill, the angle of elevation to the top of the tower is 56° and the
angle to the bottom of the tower is 51°. What is the distance from the given point to the
bottom of the tower?
a. 74 feet
b. 321 feet
c. 446 feet
d. 47 feet
Solve for x if 5^x=200
Answer:
x ≈ 3.29
Step-by-step explanation:
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
x = [tex]\frac{ln(200)}{ln(5)}[/tex]
Decimal Form:
x = 3.29202967 … ≈ 3.29 (Round to what the question asks, in this case, I rounded to 2 decimal places)
Answer:
ln200/ln5
Step-by-step explanation:
ln5^x=ln200
xln5=ln200
x=ln200/ln5
Sharina simplified the expression 3(2x – 6 – x + 1)2 – 2 + 4x. In Step 1 she simplified within the parentheses. In Step 2 she expanded the exponent.
Which is a possible next step?
Malik deposited 45% of his paycheck into his
savings account. He deposited $288 into his
savings account. How much was Malik's
paycheck?
PLEASEEEEE HELP MEEEEEE
Answer:
1. VW = 22
2. x = 87
Step-by-step explanation:
Question 1:
SU = 11 (given)
SU = ½(VW) => midsegment theorem
11 = ½(VW) => Substitution
Multiply both sides by 2
2*11 = VW
VW = 22
Question 2:
UV = x + 13
RT = x - 37
RT = ½(UV) => Midsegment Theorem
x - 37 = ½(x + 13) => Substitution
Multiply both sides by 2
2(x - 37) = x + 13
2x - 74 = x + 13
2x - 74 + 74 = x + 13 + 74
2x = x + 87
2x - x = x + 87 - x
x = 87
(2+5i)+(1+2i)
Please
Answer:
3 + 7i
Step-by-step explanation:
(2+5i)+(1+2i) =
= 2 + 1 + 5i + 2i
= 3 + 7i
can you please help i need it today
She should use the $10 off coupon because she saves more money.
How did you find the length of the a sides?
Answer:
So If This Is Area You Take The Top Number And Subtract It By The Bottom Number To Get the Sides
Step-by-step explanation:
Help plz and divide show how u divided pls I’m taking test
Answer:
its c i think. 3/5 is 60%
Step-by-step explanation:
1/5= 20% so 20%x3=60%
Janae solved the equation 3.67 = c − 2.13 , and found the value for c. Janae's solution was c =1.54 Do you agree or disagree with her solution. Explain. Show your work.
Answer:
Solution;
given equation : 3.67 = c - 2.13
On solving equation, we get
c = 3.67 +2.13
c = 5.8
Hence, Janae solution is incorrect. So I disagree.
The total cost of a pair of shoes and a shirt was $81.59. If the price of the pair of shoes was $0.91 less than the shirt, what was the price of the pair of shoes? Express your answer as a simplified fraction or a decimal rounded to two places.
Answer:
$40.34
Step-by-step explanation:
x+(x+.91)=81.59
2x+.91=81.59
2x=80.68
x=40.34
Quina is cooking fish for a group of travelers. Quina has 78 huge fish, and each fish can feed 3 travelers.
How many travelers can Quina feed?
Choose 1 answer:
(Choice A)
Quina can feed 26 travelers, because 78÷3=26.
(Choice B)
Quina can feed 22 travelers, because 78÷3=22.
(Choice C)
Quina can feed 234 travelers, because 78×3=234.
I will give Brainly plzzz ASAP
Answer:
Im pretty sure the answer would be 6
Step-by-step explanation:
Just take 42 and divide by 7 to get x
Answer:
did you finish this already
What is the length of the altitude of the equilateral triangle below?
30
6V3
63
60" 90
60"
Зүз
33
О
А. 81
В. 9
ОО
С. 33
D. 08
ОО
Е. З
о
E. 93
Answer:
its 63.
Step-by-step explanation:
The length of the altitude of the equilateral triangle is a√3/4 units.
What is a triangle?A triangle is a two - dimensional figure with three sides and three angles.The sum of the angles of the triangle is equal to 180 degrees.∠A + ∠B + ∠C = 180°Given is to find the length of the altitude of the equilateral triangle.
An equilateral triangle is a triangle whose all sides are equal. All the angles of a given equilateral triangle are 60 degrees.
The length of the altitude of the equilateral triangle can be found out using the Pythagoras theorem.
Draw a median from one vertex on the opposite side to that vertex and apply Pythagoras theorem to one of the right triangle.
We can find the length of the altitude to be -
L = a√3/4
Therefore, the length of the altitude of the equilateral triangle is a√3/4 units.
To solve more questions on triangles, visit the link-
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FINAL PROJECT 2
Fill in the missing areas for Claire's garden table:
x 1 2 3 4 5
y 14 13 12 11 10
A 50
If you have the answers for this one please list all of them below with the answer for the table (if you took the test)
Answer:
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} \ \\ y & {14} & {13} & {12} & {11} & {10} \ \\ A & {14} & {26} & {36} & {44} & {50}\ \end{array}[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} \ \\ y & {14} & {13} & {12} & {11} & {10} \ \\ A & { } & { } & { } & { } & {50}\ \end{array}[/tex]
Required
Complete the table of Areas
Using the complete column:
Where x = 5, y = 10 and A = 50,
We can deduce that, the area is calculated as:
[tex]A = 5 * 10 = 50[/tex]
i.e.
[tex]A = x * y[/tex]
So, for other values of x and y, the area is calculated as thus:
[tex]x = 1; y = 14[/tex]
[tex]A = 1 * 14 = 14[/tex]
[tex]x = 2; y = 13[/tex]
[tex]A = 2 * 13 = 26[/tex]
[tex]x = 3; y=12[/tex]
[tex]A = 3 * 12 = 36[/tex]
[tex]x =4;y =11[/tex]
[tex]A = 4 * 11 = 44[/tex]
So, the complete table is:
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} \ \\ y & {14} & {13} & {12} & {11} & {10} \ \\ A & {14} & {26} & {36} & {44} & {50}\ \end{array}[/tex]