The required 80% confidence interval is (46.15, 49.85).
What is a confidence interval?In frequentist statistics, a confidence interval is a range of estimates for an unknown quantity.
The most common confidence level is 95%, but when calculating confidence intervals, other levels, such as 90% or 99%, are also occasionally employed.
So, we know that:
n = 32
χ' = 48
s = 8
Create an 80% confidence interval using the equation below:
[tex]\left(\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}\right)[/tex]
To determine the critical value t for n-1 degrees of freedom and 1 -cl level of significance, use the formula below:
[tex]t_{0.2, d f=31}=\pm 1.309[/tex]
Create the confidence interval now:
[tex]\begin{aligned}& \left(48 \pm 1.309 \times \frac{8}{\sqrt{32}}\right) \\& (48 \pm 1.85) \\& (46.15,49.85)\end{aligned}[/tex]
Therefore, the required 80% confidence interval is (46.15, 49.85).
Know more about the confidence interval here:
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A satellite system consists of 4 components and can function if at least 2of them are working. If each component independently works with probability 0.8, what is the probability the system will function?
Answer:
X follows binomial distribution with n=4, p=0.6, q= 0.4. To make the system function adequately, at least 2 components should work well.
Step-by-step explanation:
Hope this helps
Answer:
0.9728
Step-by-step explanation:
We have 2 options for the system to fail - no components work, or only one works.
The probability that no components work is:
[tex]0.2^4 = 0.0016[/tex]
The probability that one SPECIFIC component works and the others failed is:
[tex]0.2^3 \cdot 0.8 = 0.0064[/tex]
And because there's 4 components, the chance that EXACTLY ONE works but the others don't is:
[tex]4 \cdot 0.0064 = 0.0256[/tex]
So we sum the probabilities:
[tex]P_{failure} = 0.0016 + 0.0256 = 0.0272\\P_{works} = 1 - P_{failure} = 0.9728[/tex]
A marketing research company desires to know the mean consumption of milk per week among people over age 45. They believe that the milk consumption has a mean of 4.2 liters, and want to construct a 98% confidence interval with a maximum error of 0.08 liters. Assuming a standard deviation of 0.6 liters, what is the minimum number of people over age 45 they must include in their sample
Answer:
The minimum number of people over age 45 they must include in their sample is 305.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 0.6 liters
This means that [tex]\sigma = 0.6[/tex]
What is the minimum number of people over age 45 they must include in their sample?
This is n for which M = 0.08. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.08 = 2.327\frac{0.6}{\sqrt{n}}[/tex]
[tex]0.08\sqrt{n} = 2.327*0.6[/tex]
[tex]\sqrt{n} = \frac{2.327*0.6}{0.08}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*0.6}{0.08})^2[/tex]
[tex]n = 304.6[/tex]
Rounding up:
The minimum number of people over age 45 they must include in their sample is 305.
2 1/5 + 6 4/5 pls help
Answer:
2 1/5 + 6 4/5
= 2/5 + 24/5
= 26/5
= 5.2
Answer:
[tex]8\frac{5}{10}[/tex]
Step-by-step explanation:
[tex]2 + 6 = 8\\\frac{1}{5} + \frac{4}{5} = \frac{5}{10}[/tex]
Let me know if this helps!
What is (14x^2– 27x+9) / (7x-3)?
A. 7x-3
B. 2x-3
C. -211x+9
D. 2x-33
Answer:
B. 2x - 3
Step-by-step explanation:
[tex] \rm \frac{ {14x}^{2} - 27x + 9}{7x - 3} [/tex]
[tex] \rm = \frac{ \cancel{(7x - 3)}(2x - 3)}{ \cancel{7x - 3}} [/tex]
[tex] \boxed{ \rm \bold{= 2x - 3}}[/tex]
Answer:
[tex]\tt{}2x - 3[/tex]
Step-by-step explanation:
[tex] \tt{} \frac{(14 {x}^{2} - 27x + 9) }{(7x - 3)} [/tex]
[tex] \tt{} \frac{14 {x}^{2} - 6x - 21x + 9 }{7x - 3} [/tex]
[tex]\tt{} \frac{2x \times (7x - 3) - 3(7x - 3)}{7x - 3 } [/tex]
[tex]\tt{}2x - 3[/tex]
Whisper is exercised twice a day.
The first time is for 30 minutes.
The second time is for 11 hours.
i. Write down the fraction of a day that Whisper is exercised.
Write your answer in its simplest form.
ii.
Write down the fraction of a day that she is not being exercised.
Answer:
I:23/48
ii 25/48
Step-by-step explanation:
30min=0.5hr
total time exercised: 11+0.5=11.5hr
Divided by total hours of a day:
11.5/24=115/240=23/48
ii:(48-23)/48
Week 5 Test Taking skills, Page 2
Name
3
Rodrigo bought a sheet of shark stickers. He used 8 of the 32 stickers to decorate his science project about
sharks.
Shark Stickers
DO
How many shark stickers did Rodrigo use on his science project?
A
24
B
18
с
20
D
30
It’s number 3
Answer:
20
Step-by-step explanation:
5/8 of 32
5/8×32=20
remember of means multiply
HOPE THIS HELP YOU HAVE A NICE DAY OR NIGHT
What is the 20th term of the arithmetic sequence
3, 9, 15, 21, 27, ...?
Answer: 117
Step-by-step explanation:
first comment on first response!!! Thank you btwww!
IF YOU ANSWER ALL THESE QUESTIONS I WIL LGIVE YOU BRAINIEST AMD 40 POINTS COME UP WITH PROBLEMS THANKS
Answer:
WHY YOU ARE ALWAYS SAY THAT CAN YOU WHOLE QUESTION..
Round 329,167 to the nearest hundred
Answer:
329,200
Step-by-step explanation:
Answer:
329,200
Step-by-step explanation:
What is the value of 4+2 +6r – tr when t =
=
- 3 and r = 5?
Enter your answer in the box.
you first substitute your values t and r ...Use BODMAS method ...Your final answer must be 51
help me please I will mark 5 stars please it is urgent
Answer:
a) 3sec
b) highest point of 50
c) at 0 by 8 sec
HELP ASAP A factory makes car batteries. The probability that a battery is defective is is.
If 400 batteries are tested, about how many are expected to be defective?
A. 25
B. 40
C. 16
D. 375
375 is the ansewer wwrhttttttttttttttttttt
Answer:
25
Step-by-step explanation:
This graph represents the height a baseball travels in t seconds.
How long is the height of the ball increasing?
0.5 seconds
1 second
2.4 seconds
30 seconds
Suppose y varies directly with x and inversely with z. If y = 14 when x = 7 and z = 3, what is x when y = 3 and z = 8? Use the step-by-step process you learned to solve this problem.
Step 1: Set up the correct type of variation equation.
y =
✔ kx/z
Step 2: Determine the constant of variation.
k =
Answer:
The constant of variation k is 6 and the value of x is 4.
Step-by-step explanation:
What is constant of variation?
The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.
What is direct variation?
A direct variation is a proportionality relationship in which two quantities follow a direct relationship.
What is inverse variation?
Inverse variation states when one variable increases then the other variable decreases.
Given,
y=14 when x=7 and z=3
The variation equation is,
y=kx/z
Inputting the values,
14=(k*7)/3
14*3=7*k
42=7k
k=6
When y=3, z=8 we will find x.
y=kx/z
3=6*x/8
3*8=6*x
x=24/6
x=4
Hence, the value is 4.
To know more about constant of variation, direct variation, inverse variation here
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It takes Paul 9 hours longer than Li Ming to paint a house. Working together they can do the job in 20 hours. How long would it take Li Ming, working alone, to paint the house ?
Li Ming can paint the whole house in 10 hours
Please help I’ll mark you as brainliest if correct!
Answer:
B
Step-by-step explanation:
brainliest?
blank plus 1/2 equals to 2/3
Answer:
1/6 + 1/2 = 2/3
Step-by-step explanation:
A $45 pair of shoes is on sale for 20% off. How much money is saved?
Answer:
$9
Step-by-step explanation:
https://studio.code.org/projects/flappy/cYGc2S_X9-cgWtBUmJ5BJta5xku7iqyon0wzrKhC-Do
Answer:
so fun and amazing!
Step-by-step explanation:
Determine whether each ordered pair is a solution of the system of linear equations.
3y = 6x + 12
2x - y = -4
a. (-3,2)
b. (0,4)
a. Is (-3,2) a solution?
0 Yes
Ο Νο
b. Is (0,4) a solution?
O No
0 Yes
Answer:
(0,4)
Step-by-step explanation:
The given equations are :
3y = 6x + 12
2x - y = -4
If (-3,2) be the solution of the above equations,
3(2) = 6(-3) + 12
6 = -18+12
6≠ -6
2x - y = -4
2(2) -(-3) =-4
4+7 = -4
11 ≠ -4
No, (-3,2) is not the solution.
Similarly, put (0,4) in the abve equations,
3(4) = 6(0) + 12
12 = 12
and
2(0) - 4 = -4
-4 = -4
Hence, (0,4) is a solution of the given equations.
PLEASE HELP !!!!!
What is the value of the missing angle?
Answer:
B
Step-by-step explanation:
180 - 100 = 80
80 = 30 = 110
180 - 110 = 70
Answer:
B
Step-by-step explanation:
100-30=70° Remeber this is a right triangle
Select the correct answer.
The figure PQRSTU represents the shape of the parking lot at a shopping mall. What is the area of the parking lot?
A.
834 square feet
B.
918 square feet
C.
984 square feet
D.
1,068 square feet
Reset
Answer:
Is there an image? I cant figure it out without the image
Step-by-step explanation:
Find the area of the sector.
Answer:
D. 158.4 km²
Step-by-step explanation:
Area of sector = θ/360 * πr²
Where,
θ = 150°
r = 11 km
Substitute
Area = 150/360 * π * 11²
Area = 158.38863 ≈ 158.4 km² (nearest tenth)
Please helpppp meeee
Raymond kept track of the number of hours that he spent practicing the piano each week for several weeks. He spent 2, 4, 8, 6, and 5 hours. What is the range of the data set? B. 5 hours O A. 2 hours O O O D. 6 hours C. 8 hours
Brainliest for correct answer
Answer:
V =1884 in ^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = pi ( 10) ^2 * 6
V = pi ( 600) in^3
Using 3.14 for pi
V = 3.14 * 600 in ^3
V =1884 in ^3
500 people are asked if they drink coffee.
9
10 say Yes.
20% of the people who say Yes drink at least three cups each day.
(b)
What fraction of the 500 people drink at least three cups of coffee each
day?
Give your answer in its simplest form.
Answer:
Step-by-step explanation:
2/10
g Radio and television stations often air controversial issues during broadcast time and ask listeners and viewers to indicate their agreement or disagreement with a given stand on the issue. A poll is conducted by asking those listeners and viewers who agree to call a certain 900 telephone number and those listeners and viewers who disagree to call a second 900 telephone number. All respondents pay a fee for their calls. Does this polling technique result in a random sample
Answer:
NO, it does not.
Step-by-step explanation:
From the information provided, we know that the surveying method for the polling depends on the no. of calls got on the two sorts of 900 phone numbers.
This surveying strategy doesn't address a random sample in light of the fact that the viewers who see the show can be restricted. Additionally, among the viewers of the show, the reactions depend on viewers who intentionally approach to offer or air their opinion. Therefore, the acquired sample doesn't address a random sample and specifically, we can posit that the sample occurs to be a voluntary sample.
The mixed number 2 5/6 is equivalent to a fraction with a
denominator of 6.
What is the missing numerator in the equivalent
fraction?
Answer:
6 x 2 = 12 then add 5, answer is 17
Help,,,,,,,,,,,,,,,........