The batteries produced in a manufacturing plant have a mean time to failure of 30 months with a standard deviation of 2 months. I select a simple random sample of 400 batteries produced in the manufacturing plant. I test each and record how long it takes for each battery to fail. I then compute the average of all the failure times. The sampling distribution of is approximately:
Answer:
By the Central Limit Theorem, the sampling distribution is approximately normal, with mean 30 and standard deviation 0.1.
Step-by-step explanation:
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
The batteries produced in a manufacturing plant have a mean time to failure of 30 months with a standard deviation of 2 months.
This means that [tex]\mu = 30, \sigma = 2[/tex]
Sample of 400 batteries. The sampling distribution of is approximately:
So [tex]n = 400, s = \frac{\sigma}{\sqrt{n}} = \frac{2}{\sqrt{400}} = 0.1[/tex]
By the Central Limit Theorem, the sampling distribution is approximately normal, with mean 30 and standard deviation 0.1.
A simple random sample of 140 residents in a certain town was polled the week after the Super Bowl. 75 of them reported that they watched the game on TV. a) Construct the 95% CI for the proportion of people that watched Super Bowl. b) The prognosis stated that the proportion of people watching the game is 48.1%. Does this prognosis contradict your findings
Answer:
a) The 95% CI for the proportion of people that watched Super Bowl is (0.4531, 0.6183).
b) 48.1% = 0.481 is part of the confidence interval, which means that this prognosis does not contradict the findings.
Step-by-step explanation:
a) Construct the 95% CI for the proportion of people that watched Super Bowl.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
75 out of 140 watched the Super Bowl:
This means that [tex]n = 140, \pi = \frac{75}{140} = 0.5357[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5357 - 1.96\sqrt{\frac{0.5357*0.4643}{140}} = 0.4531[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5357 + 1.96\sqrt{\frac{0.5357*0.4643}{140}} = 0.6183[/tex]
The 95% CI for the proportion of people that watched Super Bowl is (0.4531, 0.6183).
b) The prognosis stated that the proportion of people watching the game is 48.1%. Does this prognosis contradict your findings
48.1% = 0.481 is part of the confidence interval, which means that this prognosis does not contradict the findings.
Which of the following equations represents a line that is parallel to the line 1 point
with the equation below?*
y = -3x +4
A. 6x+2y=15
B. 3x-y=7
C. 2x-3y=6
D. X+3y=1
Step-by-step explanation:
step 1. I assume the question is which of the following equations is parallel to y = -3x + 4
step 2. parallel equation have identical slopes (m)
step 3. 6x + 2y = 15 or y = -3x + 15/2 (solve for y)
step 4. 3x - y = 7 or y = 3x - 7 (solve for y)
step 5. 2x - 3y = 6 or y = (2/3)x - 2 (solve for y)
step 6. x + 3y = 1 or y = (-1/3)x + 1/3
step 7. since y = mx + b we want m to be the same
step 8. the answer is A since they both have the same slope.
Write the fraction 28 in its simplest form.
70
Answer: 2/5
Step-by-step explanation: 28/70 ÷ 12/12 = 2/5
The simplest form of the given fraction is 2 / 5
What is a fraction?A fraction represents part of a whole. When something is broken up into a number of parts, the fraction shows how many of those parts you have.
Given is a fraction, 28 / 70, we have to convert it into its simplest form,
28 / 70
= 2(14) / 5(14)
= 2 / 5
Hence, the simplest form of the given fraction is 2 / 5
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Please help I put a screenshot of the assignment
Answer:
78.5ft^2
Step-by-step explanation:
calculations done on a calculator
Answer:
78.5
Step-by-step explanation:
4 x 2.5 = 10 ft
4.5 x 2.5 = 11.25
4.5 x 4 = 18
18 + 10 + 11.25 = 39.25
39.25 x 2 = 78.5
Find the exact value of cos A in simplest radical form.
inequalities
16 + j ≥ 29; 13, 12, 11
show work
Find the measure of:
Answer:
4.8x10
Step-by-step explanation:
Recall the study about anchoring , in which students estimated the population of Milwaukee aft er some had been told about Chicago and others about Green Bay.
a. Describe in words the parameter(s) of interest in the context of this study.
b. In the context of the parameter(s) described in part (a), express the null and alternative hypotheses for testing whether the class data give strong evidence in support of the anchoring phenomenon described above. If you use symbols, make sure to defi ne them.
c. Check whether the conditions for the validity of the theory-based t-test to compare two means are satisfi ed here.
d. Use appropriate technology (an applet or a statistical soft - ware package) to conduct a t-test of signifi cance of the hypotheses that you stated in part (b). Report the test statistic and p-value.
e. State your conclusion in the context of the study, being sure to comment on statistical signifi cance.
f. Determine and interpret the 95% confi dence interval using a theory-based approach for the parameter(s) of interest in the context of the study.
g. Comment on causation and generalization for this study.
Answer:
hduyvhudsnuv uisdhavusdhvu wujwfhuvudf hu cvhfdyu yf u fe7tg76iufe ygy
Step-by-step expleanation:
tgdwtydttfdtydfdsgfdgfdsvsfvgffgfg fg fg f gf gfg
fg
fg
g
fg
f
PLEASE HELP I WILL GIVE BRANLIEST IF YOUR ANSWER IS CORRECT!
Answer:
1:4
2:8
3:12
4:16
Step-by-step explanation:
what is the value expression 26+22÷12 pls help me
Answer:
As a decimal : 27.833
As a fraction : 167/6
Step-by-step explanation:
26 + 22/12
=
26/1 + 22/12
=
26/1 + 11/6
=
156/6 + 11/6
156 + 11 / 6
=
167/6
or as a decimal 27.833
Hope this helps!
Please help I’ll mark you as brainliest if correct!
my work is down below.Please answer it!
Answer:
1. A≈ 78.54
2. A≈201.06
Step-by-step explanation:
1) A=πr2=π·52≈78.53982
2)
A=1
4πd2=1
4·π·162≈201.06193
Given the equation 2 Square root of x minus 5 = 2, solve for x and identify if it is an extraneous solution
Answer:
Step-by-step explanation:
2√(x-5) = 2
√(x-5) = 1
x-5 = 1
x = 6
what is the opposite of –|−8|?
Answer:
it should be |8| or just 8 because there can not be a negative in the absolute value sign. pretty sure but not 100%
Answer:
|8|
Step-by-step explanation:
that is your answer :D
Daniel opened a savings account with $1600 that pays no interest. He deposits an additional $200 each week thereafter. How much money would Daniel have in the account 25 weeks after opening the account?
[tex] \frac{12x + 40}{8x} \div \frac{24x + 80}{8} [/tex]
what are the steps to solving this?
In the diagram, JK || GI. If the ratio of HJ to JG is 3 to 1, then what is the ratio of HK to KI?
The expression JK||GI implies line JK and GI are parallel lines
The ratio of HK : KI is 3 : 1
What is a ratio?A ratio is used to show the relationship between two related quantities
How to determine the ratio?The given parameter is:
HJ : JG = 3 : 1
Given that JK||GI , then it means that:
HJ : JG = HK : KI
This gives
HK : KI = 3 : 1
Hence, the ratio of HK : KI is 3 : 1
Read more about equivalent ratios at:
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a gift box in the shape of a rectangular prism measures 8in by 8in by 10in. what is the least amount of wrapping paper needed to wrap the gift box?
Answer:
Step-by-step explanation:
The surface area of a rectangular prism is
A=2(xy+xz+yz), where x,y,z are the dimensions, in this case
A=2(8(8)+8(10)+8(10))
A=2(64+80+80)
A=2(224)
A=448in^2
So the minimum amount of wrapping paper is 448in^2
A school needs to buy new notebook
and desktop computers for its
computer lab. The notebook
computers cost $400 each, and the
laptop
computers cost $150 each. How
much would it cost to buy 13
notebooks and 19 desktop
computers? How much would it cost
to buy
n notebooks and d desktop
computers?
Total cost, 13 notebooks and 19
desktop computers:
Total cost, n notebooks and d desktop
computers:
Answer:
so if they need 400 nc and they need 13 you need to multiply which is 5200 alr now same thing with the other 150 and they need 19 you get 2850 now all together you get that's 8050 hope this helped
6 tickets for 48.00 dollars what is the unit price?
Answer:
8
Step-by-step explanation:
that's a six tickets for $48 there for F1 tickets we don't know the price of each ticket...divide 48/6
Please help me with this question
9514 1404 393
Answer:
24 cm
Step-by-step explanation:
The perimeter of the left-side triangle is ...
20 +25 +15 = 60 cm
The scale factor to the right-side triangle is the ratio of corresponding sides. The scale factor of perimeters is the same.
XZ/LN = perimeter(XYZ)/perimeter(LMN)
6/15 = P/(60 cm)
P = (60 cm)(6/15) = 24 cm
The perimeter of ΔXYZ is 24 cm.
Help me out thanks !!!!!!
Answer:
a = 12
Step-by-step explanation:
as C^2 = A^2 + B^2
by Pythagoras theorem
so
A^2 = C^2 - B^2
= 13^2 - 5^2
= 169- 25
144
as 12^2 is equal to 144
hence side a is equal to 12
Answer:
[tex]h^2 = p^2 + b^2 \\ {13}^{2} = {p }^{2} + {5}^{2} \\ 169 = {p }^{2} + 25 \\ 169 - 25 = {p}^{2} \\ 144 = {p}^{2} \\ \sqrt{144} = p \\ 12 = p \\ p = 12[/tex]
7
Carly has a bank account with a balance of $3,575. The account pays simple interest at a rate of
4.15%. How long will it take for the account to grow to $7000? Round to the nearest year.
Answer:
It will take 23 years for the account to grow to $7000.
Step-by-step explanation:
Simple Interest
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
Carly has a bank account with a balance of $3,575.
This means that [tex]P = 3575[/tex]
The account pays simple interest at a rate of 4.15%.
This means that [tex]I = 0.0415[/tex]
How long will it take for the account to grow to $7000?
[tex]T = 7000[/tex]
The interest is:
[tex]T = E + P[/tex]
[tex]E = T - P = 7000 - 3575 = 3425[/tex]
Now we have to find t.
[tex]E = P*I*t[/tex]
[tex]3425 = 3575*0.0415*t[/tex]
[tex]t = \frac{3425}{3575*0.0415}[/tex]
[tex]t = 23.1[/tex]
Rounding to the nearest year, it will take 23 years for the account to grow to $7000.
If a blue and a red dice are rolled, what is the probability of rolling a sum greater than 4?
Answer:
33/36 or 11/12
Step-by-step explanation:
Answer:
The "successful" rolls are 5 and 6. That's two out of six choices, so the probability is 2/6 or 1/3.
Step-by-step explanation:
Hope this helps!!! <3
(7.11 x 10') (2.97 x 10-3)
Answer:
The answer is 1898.37
if you click the image it will show you how to solve the equation. I hope this helps you.
what does 4n+3(n-5)+2 equal
Answer:
7n-13
Step-by-step explanation:
Simplify
4n+3(n-5)+2
4n+3n-15+2
Add The Numbers
4n+3n-15+2
4n+3n-13
Combine Like Terms
4n+3n-13
7n-13 Solution 7n-13
Using Heron's Formula, find the Area.
Sides are 7 13 8
Answer:
10.3
Step-by-step explanation:
hope this helps, if any genius answers as well, give brainliest to them
Answer:
[tex]\Huge\boxed{A=24.25}[/tex]
Step-by-step explanation:
Herons Formula:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where s = semi perimeter ( perimeter of triangle divided by 2)
and a,b and c = triangle side lengths
Before we can solve we need to calculate the semi perimeter
7 + 13 + 8 = 28
then we divide by 2
28/2=14
so the semi perimeter is 14
now we plug in everything into the formula
[tex]A=\sqrt{14(14-13)(14-8)(14-7)} \\14 - 13=1\\14-7=7\\14-8=6\\A=\sqrt{14(1)(6)(7)} \\14*1=14\\14*7=98\\98*6=588\\A=\sqrt{588} \\\sqrt{588} =24.24871131[/tex]
so we can conclude that the area of the triangle is 24.24871131
our final step is to round to the nearest hundredth
A = 24.25
3. What is the value ofy?
A. 3
C. 6
B. 8
D. 12
Determine the measure of angle C using a trigonometric ratio.
Answer:
34.836
Step-by-step explanation:
sin(C)=opp/hyp=16/28=4/7
C= inverse sin = 34.836 deg
The angle of the right-angled triangle using trigonometric ratio is 34.84°.
What is trigonometry?Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
The diagram shows the right-angled triangle.
The hypotenuse side, h = 28
The perpendicular side, p =16
The trigonometric ratio that relates hypotenuse side and the perpendicular side is sine θ.
[tex]Sine \theta=\frac{perpendicular}{hypotenuse}[/tex]
⇒ [tex]Sine\theta = \frac{16}{28}[/tex]
⇒ [tex]Sine \theta=0.5714[/tex]
⇒ [tex]\theta = Sine^{-1} (0.5714)[/tex]
⇒ [tex]\theta = 34.84[/tex]
Hence we can conclude that the angle of the right-angled triangle using trigonometric ratio is 34.84°.
Learn more about trigonometry here
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