Answer:
The calculated value Z = 1.548 < 2.326 at 0.01 level of significance
The Null Hypothesis is accepted
There is no change in the weekly production
Step-by-step explanation:
Step(i):-
Given that the mean Population(μ) = 200
Given that the standard deviation of the Population(σ) =16
Given that the mean of the sample (x⁻) = 203.5
Given that the size of the sample(n) = 50
Level of significance = 0.01
Critical value Z₀.₀₁ = 2.326
Null hypothesis : (μ) = 200
Alternative Hypothesis : (μ) ≠200
Step(ii):-
Let 'X' be a random variable in a normal distribution
Test statistic
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{203.5 -200}{\frac{16}{\sqrt{50} } }[/tex]
Z = 1.548
The calculated value Z = 1.548 < 2.326 at 0.01 level of significance
The Null Hypothesis is accepted
Final answer:-
There is no change in the weekly production
Find the circumference of the circle and round to the nearest tenth
Answer:
The circumference is 45.2yd
Step-by-step explanation:
Given
[tex]d = 14.4[/tex] --- diameter
Required
Determine the circumference
The circumference is calculated as:
[tex]C =\pi d[/tex]
So, we have:
[tex]C =\pi * 14.4[/tex]
Take pi a 3.14
[tex]C =3.14 * 14.4[/tex]
[tex]C =45.216[/tex]
Approximate
[tex]C =45.2yd[/tex]
Each day a manufacturing plant receives a large shipment of drums of Chemical ZX-900. These drums are supposed to have a mean fill of 50 gallons, while the fills have a standard deviation known to be 0.6 gallon. Suppose the mean fill for the shipment is actually 50 gallons. If we draw a random sample of 100 drums from the shipment, what is the probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons
Answer:
0.9544 = 95.44% probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons.
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.
Suppose the mean fill for the shipment is actually 50 gallons. Standard deviation of 0.6 gallons.
This means that [tex]\mu = 50, \sigma = 0.6[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{0.6}{\sqrt{100}} = 0.06[/tex]
What is the probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons?
This is the pvalue of Z when X = 50.12 subtracted by the pvalue of Z when X = 49.88. So
X = 50.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{50.12 - 50}{0.06}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 49.88
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{49.88 - 50}{0.06}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that the average fill for the 100 drums is between 49.88 and 50.12 gallons.
Beetles may be the most varied order of animals. New beetle species are authenticated, completely unpredictably, at a typical rate of one every 7.0 months. A supplement to a guide is planned to be published after 20 new species have been discovered. a) What are the expected value and standard deviation of the number of months (treated as a continuous measure of time) until the supplement is published
Answer:
The mean until the supplement is published is 140 months, while the standard deviation is of 11.8 months.
Step-by-step explanation:
The Poisson distribution is used to solve this question, as we have only the mean. In this distribution, the standard deviation is the square root of the mean.
In this question, we have that:
Species are discovered at a rate of once every 7 months.
A supplement to a guide is planned to be published after 20 new species have been discovered.
a) What are the expected value and standard deviation of the number of months (treated as a continuous measure of time) until the supplement is published?
Mean is: 7*20 = 140 months.
Standard deviation is [tex]\sqrt{140}[/tex] = 11.8 months.
The mean until the supplement is published is 140 months, while the standard deviation is of 11.8 months.
someone help me plzz
Answer:
1/4
Step-by-step explanation:
.
does -(-(-e) = -e?
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Answer:
wth is this
show the pic of the question
Question A researcher wants a 30 milliliter acid solution with a concentration of 8%. She has concentrations of 2% and 11%. How much of each solution must she use to get the desired concentration?
Answer:
The researcher needs 20 milliliters of 11 percent concentrated acid and 10 milliliters of 2 percent concentrated acid.
Step-by-step explanation:
Given that a researcher wants a 30 milliliter acid solution with a concentration of 8%, and she has concentrations of 2% and 11%, to determine how much of each solution must she use to get the desired concentration, the following calculation must be performed:
100 x 0.11 + 0 x 0.02 = 11
90 x 0.11 + 10 x 0.02 = 10.1
80 x 0.11 + 20 x 0.02 = 9.2
70 x 0.11 + 30 x 0.02 = 8.3
66.666 x 0.11 + 33.333 x 0.02 = 8
30 x 0.6666 = 20
Therefore, the researcher needs 20 milliliters of 11 percent concentrated acid and 10 milliliters of 2 percent concentrated acid.
HURRY AND GET BAINLESS FOR BEST ANSWER!!!How much cookie dough will each friend get if 1 1/2 pounds is split between 4 friends?
Answer: 3/8 pounds
Step-by-step explanation:
the Amount of cookie dough per person equals the total weight of dough divided by the total number of people
1 1/2 equals 3/2
so the amount of cookie dough per person equals 3/2 divided by 4
Equals 3/2 x 1/4
Equals 3/8 pounds
So each friend gets 3/8 pounds of cookie dough
there u go...
Use the figure below and 2-3 sentences to explain the following:
The side opposite angle E is side ____?
The side adjacent to angle E is side ____?
The hypotenuse is side ____?
Answer:
See below
Step-by-step explanation:
The side opposite angle E is side e (DF)
The side adjacent to angle E is side d (EF)
The hypotenuse is side f (ED)
Need help ASAP plssss
The ratio of 8:5=(?)%
Answer:
The ratio of 8:5 = 160%
Step-by-step explanation:
1. Divide the first number by the second number
2. Multiply by 100 to convert to a percentage
Which angles are supplementary to each other?
it taken 12 days for 10 men assemble a machine how long could it take for 15 men to assemble the machine?
The diameter of a tree trunk is 23 in. what is the circumference?
Answer:
72.2566311
Step-by-step explanation:
Circumference = 2πr
We don't have the radius, but we do know that half of the diameter is the radius, so 23/2 = 11.5. r = 11.5
Now, plug the radius into the equation:
2π(11.5)
Solve:
2π(11.5) = 72.2566311
Edwin buys a video game that is $55. It is on sale for 20% off, and he has to pay 10% sales tax. Is the final cost the same as a 10% discount? Why or why not?
Answer:
No If it would be 10 percent of the total would be the price tag without tax
Step-by-step explanation:
Please I’m begging help me I don’t get this question I tried solving it these past 50 minutes ILL GIVE YOU BRAINLINEST
Answer:
Monday=275
Tuesday=330
thursday=360
Friday=440
Step-by-step explanation:
Add the entire number to itself since its above 100%
then figure out 10% of the number for monday is 12.5 thats only ten so we gotta figure out 20% so 12.5x2=25
Hence its 125+125+25
250+25
275
This is for monday but this applies on all of them
square root of 10x^3yz5n21
Answer: 5
Step-by-step explanation:
The product of two consecutive positive even integers is 14 more than their sum. Set up an equation that can
used to find the two numbers and solve it.
Answer:
+/- 2 both work.
Step-by-step explanation:
Remark
To make sure they are even, you need to use 2x and 2x + 2
Equation
2x (2x + 2) = 2x + 2x + 2 + 14 Combine like terms on the right
Solution
2x(2x + 2) = 4x + 16 Remove the brackets
4x^2 + 4x = 4x + 16 Subtract 4x from both sides.
-4x -4x
4x^2 = 16 Divide by 4
x^2 = 16/4
x^2 = 4 Take the square root of both sides
x = +/- 2
Question
Does - 2 work?
2(-2)(-2*2 + 2) = 4(-2)+2 + 14
-4(-4 + 2) = - 8 +2+ 14
-4( - 2) = - 8 + 2+ 14
8 = 8
Yes it does
Suppose a polling agency reported that 48.0% of registered voters were in favor of raising income taxes to pay down the national debt. The agency states that results are based on telephone interviews with a random sample of 1033 registered voters. Suppose the agency states the margin of error for 95% confidence is 3.0%. Determine and interpret the confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt. ▼ We are 48.0% confident There is a 95% probability We are 95% confident There is a 3.0% probability We are 1033% confident We are 3.0% confident There is a 48.0% probability There is a 1033% probability that the proportion of ▼ all Americans registered voters adult Americans aged 18 or older in favor of raising income taxes to pay down the national debt is between nothing and nothing
Answer:
The 95% confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt is (45%, 51%). This means that we are 95% sure that the true proportion of all registered voters who are in favor of raising income taxes to pay down the national debt is between these two values, of 45% and 51%.
Step-by-step explanation:
A confidence interval is the sample proportion plus/minus the margin of error.
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
In this question:
Sample proportion of 48%.
Suppose the agency states the margin of error for 95% confidence is 3.0%. Determine and interpret the confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt.
48% - 3% = 45%
48% + 3% = 51%
The 95% confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt is (45%, 51%). This means that we are 95% sure that the true proportion of all registered voters who are in favor of raising income taxes to pay down the national debt is between these two values, of 45% and 51%.
i just need this solved please
2x+(7x+4)=3x-22
Answer:
All I got is this I'm sorry
Step-by-step explanation:
Exact form -13/3
Decimal form -4.3
Mixed -4 1/3
Write an equation. Putri Qis buys 8 packs of markers. Each pack contains the same number of markers. Putri Qis gave 10 markers to her brother. Then, she has 54 markers left.
Answer:
M = number of markers in a pack
8M = 54 + 10
solution:
8M = 64
M = 8 markers per pack
Can u plz help me with 7,8,9
Answer:
7 :ans is 10
8: ans is 25
9: ans is 46
Can someone help me plz.
The last one in the box is 35
Answer:
sorry I. don't. know
Measurements of a Circle
(Giving correct answer brainliest)
Answer:
B. [tex] \frac{9}{20}\pi [/tex]
Step-by-step explanation:
Central angle [tex] \theta = 81\degree [/tex]
Radius (r) = 1 unit
[tex] l(\widehat {HJ}) = \frac{\theta}{360\degree} \times 2\pi r[/tex]
[tex] l(\widehat {HJ}) = \frac{81\degree}{360\degree} \times 2\pi r[/tex]
[tex] l(\widehat {HJ}) = \frac{81}{360} \times 2\pi (1)[/tex]
[tex] l(\widehat {HJ}) = \frac{9}{40} \times 2\pi [/tex]
[tex] l(\widehat {HJ}) = \frac{9}{20}\pi [/tex]
how to write 6 and 9 together
HELP PLS HURRY
Which table represents a nonlinear function
A.) x y
2 -9
4 1
6 11
B.) x y
2 -14
4 -16
6 -18
C.) x y
2 0
4 6
6 16
D.) x y
2 -9
4 6
6 -3
Answer:
(C)
Step-by-step explanation:
please click the heart and rate excellent and brainleist to tysm❤☺️☻♨️♨️☻☺️❤
2/4 is more than 1/4?
Answer:
Yes!
Step-by-step explanation:
Yes, because 2>1.
Answer:
yes
Step-by-step explanation:
lets say you have half of a pie that counts as 2/4 or 50%
lets say you have half of a half pie that counts as a 1/4 or 25%
There are 4 boys and 2 girls from the 7th grade and 3 boys and 5 girls from the 8th grade on the soccer team. The coach will pick one captain from each grade. What is the probability that he will pick a boy from the 7th grade and a girl from the 8th grade?
Answer:
5/12
Step-by-step explanation:
P(b,7) = 4/6
P(g,8) = 5/8
4/6 x 5/8 = 20/48 (or 5/12 reduced)
Solve the system by substitution
1) Solve for r: 4= r/8
2) What symbol makes the statement true? 27×(36_6)=162
3) Solve for h: 19h=15
Answer:
1) r = 32
2) symbol is '÷'
3) h = 15/19
Step-by-step explanation:
A flagpole casts a shadow that is 50 feet long At the same time, a woman standing nearby who is five and a half feet tall casts a shadow 4 feet long How tall is the flagpole? Draw a picture to help, if needed
Show your work please :’).
Answer:
68.75 feet tall
Step-by-step explanation:
Create a proportion where x is the height of the flagpole
[tex]\frac{x}{50}[/tex] = [tex]\frac{5.5}{4}[/tex]
Cross multiply and solve for x
4x = 275
x = 68.75
So, the flagpole is 68.75 feet tall