Answer:
The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
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
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal variables:
When we subtract two normal variables, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N.
This means that [tex]\mu_1 = 6.1, s_1 = \frac{0.7}{\sqrt{125}} = 0.0626[/tex]
In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N.
This means that [tex]\mu_2 = 5.8, s_2 = \frac{1}{\sqrt{75}} = 0.1155[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 6.1 - 5.8 = 0.3[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0626^2+0.1155^2} = 0.1314[/tex]
Confidence interval:
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 - 0.9}{2} = 0.05[/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 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.645*0.1314 = 0.22[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.3 - 0.22 = 0.08N
The upper end of the interval is the sample mean added to M. So it is 0.3 + 0.22 = 0.52N
The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).
In triangle ABC, m∠A=(2x)∘, m∠B=(3x+1)∘, and m∠C=(3x−5)∘.
What is the value of x?
Answer:
x=16
Step-by-step explanation:
8x-4=180
8x=184
x= 16
A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is
h(t) = -1662 +63 + 4, where t is measured in seconds and h is the height in feet.
What is the height of the ball after 2 seconds?
Answer:
B, D, B, D
Step-by-step explanation:
Please explain step by step I dont get it.
Answer:
B
Step-by-step explanation:
minus 3 twice
-3 times 2
Answer:
B (-3 x 2)
Step-by-step explanation:
Think about it like simple multiplication. On the number line, there are two groups of 3, except the integer is actually negative. It's about the same though.
Please could somebody help me on this one
Answer:
49π
Step-by-step explanation:
Are of the circle equal π[tex]r^{2}[/tex] (where π is pi and "r" is the radius). Radius equals the diameter divided by 2. Therefore the area of this circle equals...
[tex](14 / 2)^{2}[/tex]π = [tex]7^{2}[/tex]π = 49π
89.5, 71, 75, 76, 74, 87, 89, 71, 85
mode = ?
Answer:
mode of this question is 71
Answer:
71
Step-by-step explanation:
because mode is the number that occurs most frequently
Trina is making a friendship necklace at summer camp using 1.6 cm beads. What is a reasonable estimate for the length if she uses 24 beads? *
A.22.4 cm
B.40 cm
C.33.8 cm
D.38.4 cm
Suppose there are n people on a bus. At the next stop, 9 more people get on the bus. No one gets of the bus. Draw a bar diagram to model the number of people now on the bus. Use this model to write an algebraic expression for the number of the people now on the bus.
Answer:
Algebaric Expression & Bar Diagram graphic representation of number of people in bus.
Step-by-step explanation:
No. of people on bus = n
After 9 more boarding & no one deboarding the bus , no. of people = n + 9
Bar diagrams is graphical method for presentation of data. Presenting the given in bar diagram :
what is the range of the function in this table
Answer:
B
Step-by-step explanation:
RANGE are the Y values
Answer:
b
Step-by-step explanation:
1. The parent function f(x) = x2 was
transformed to create the graph shown below.
x
Which function best represents the
transformation?
A f(x) = 3x2 - 1
B f(x) - 3x +1
c/(x) = $x-1
D) = -1 - 3
find the 12th term of the geometric sequence show below x^2, -2x^6, 4x^10
A sofa can ve purchased for 890.00 cash or by making 12 monthly payments of 92.00. How much would be saved by paying cash?
Answer: $214
Step-by-step explanation:
First find how much you would have to pay if you payed $92 for 12 months. It would be 1104 (12 times 92)
Then you have to substract how much it would cot to pay by cash rather than paying $92 for 12 months. ( 1104-890 = 214)
Your answer is $214. You would save $214 if you pay by cash.
I hope this helps! May God bless you! :)
The normal rainfall in September for Denver is 1.24 inches. The normal rainfall for Miami in September is 7.63 inches. The normal rainfall in January for Miami is 2.01 inches. The normal rainfall in January for Denver is 6.91 inches.
To the nearest tenth of an inch, how much more rain does Miami get in September than it gets in January?
Answer:
5.60 inches
Step-by-step explanation:
7.63 - 2.01 = 5.62
5.62 ≈ 5.6
Tell me if there is any missing information in the question because the information for Denver seems useless and there probably something missing
Jennifer. Wants to wrap her Mother’s Day present in pink wrapping paper the wrapping paper cost $0.09 per square inch. How much will it cost her to wrap the present
24 swimmers are swimming in the pool. 9 of them are female. What fraction of swimmers are male?
Answer:
5/8 of swimmers in pool are male
Step-by-step explanation:
24 total swimmers
9 female so 9/24
15 male so 15/24
simplify 15/24
5/8 of swimmers in pool are male
A sample of 68 college students yields a mean annual income of $3248 and a standard deviation of $885. Find the margin of error in estimating μ at the 99% level of confidence.
Answer:
can put this solution on YOUR website!
margin of error is t(0.995 df=67)*s/sqrt(n)
t=2.65
the margin of error is 2.65*885/sqrt(68)=$284.40
Yesterday, a movie theater sold 269 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all the movie theater made $494 from
popcom sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.
The movie theater sold large bags of popcorn and small bags of popcorn.
Answer:
S=194, L=75 L+S=269, 4L+1S=$494
Step-by-step explanation:
Sara is mong a call. One of the finie piece she is using is 1 inches 3
inches. She will need 20 of the pieces. How many fear of fabric will she need
fispatam
Answer:
What are you even asking?
17
11
S
3
18
If the median is 17, which number could s be?
7
18
Answer:
s=18
Step-by-step explanation:
the median is 17(middle number)
It goes from smaller to bigger
2 numbers onthe left of 17 and 2 numbers on the right of 17
3 11 17 18 18
Answer:
it would be 18
Step-by-step explanation:
18 being the answer makes 17 the middle it has to be more than 17 and it is 18
• (1,7)
- 10
(0,0)
10
D
A. y = 7x
O B. y = 3x
O C. y = 21x
OD. y=-3x
O E. Y= 1/5x
O E y = -7x
Jim and Jabu join a gym. Jim's gym take R150 deposit,and he pays R120 monthly. Jabu's gym takes no deposit, but his monthly payment is R150. They compare their total payments after four months, after five months and after six months.
3.1 Reasoning
3.2 Number sentence
Answer:
What should I answer?
Step-by-step explanation:
Jim's payment is more than Jabu's after four months and Jabu's payment is more than Jim’s after five months.
It is given that Jim’s gym takes a deposit of 150 and a monthly charge of 120.
Let x be the number of months for which both are paying the charges.
Then, Jim's total charge=150+120x.
Now, Jabu’s gym takes no deposit and takes a monthly charge of 150.
Jabu’s gym total charge=150x
Substitute x=4 in the obtained expression to determine the total payment of both after four months.
Jim's total charge=150+120(4)
=150+480
=620
Jabu’s gym total charge=150(4)
=600
So, Jim's payment is more than Jabu after four months.
Substitute x=5 in the obtained expression to determine the total payment of both after five months.
Jim's total charge=150+120(5)
=150+600
=750
Jabu’s gym total charge=150(5)
=750
So, Jabu's payment is more than Jim’s after five months.
Therefore, Jim's payment is more than Jabu's after four months and Jabu's payment is equal to Jim’s after five months.
To learn more about the deposit visit:
https://brainly.com/question/22697743.
#SPJ2
7. Find S 14 for the arithmetic sequence. 101+98+95+92+..
Step-by-step explanation:
[tex]S _{n} = \frac{n}{2} (2a + (n - 1)d) \\ S _{14} = \frac{14}{2} ((2 \times 101) + (14 - 1) \times -3) \\ =1,141[/tex]
Which inequality is true (I ready diagnostic)
Answer:
Step-by-step explanation:
I am sorry but please give detailed question
Answer:
i'd be happy to help you, but there isn't an image attached.
Step-by-step explanation:
HELPPP 30PTS FOR THIS
Answer:
pucha no se
Step-by-step explanation:
Answer:0.08
Step-by-step explanation:4756454434232
What is the correct value for x , in the equation, 4x + 12 = 60?
Answer:
x = 12
Step-by-step explanation:
im 100% sure i hope this helps :)
Answer:
[tex]4x + 12 = 60 \\ 4x = 60 - 12 \\ 4x = 48 \\ x = \frac{48}{4} \\ x = 12[/tex]
=> 12 IՏ Tᕼᗴ ᑕOᖇᖇᗴᑕT ᗩᑎՏᗯᗴᖇ.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
whats 3/10 out of 140?
Answer:
you have got your mark in fraction.
Answer: the answer is 42.
Step-by-step explanation:
This is how you solve.
Take 140 and divide by 10.
You would get 14.
then, times 14 by 3 or add it 3 times.
14+14+14 is equal to 42.
hope This helped!
PLEASE HELP !
Someone has offered you a wager on the outcome of a die roll. You will pay him
$100 for each time the standard, six-sided die lands on one, and he will pay you $30 for each time the die lands on any other number. Without your awareness, he has loaded the die so that it has a 40% change to land on the number one, and besides
that an equal change to land on any of the values 2 through 6.
What is the expected value of one round of gambling in this scenario?
-$12
-$32
$2
-$22
You'll lose on average $22 per roll.
====================================================
Explanation:
Normally there is a 1/6 chance to land on any given side of a standard die, but your friend has loaded the die in a way to make it have a 40% chance to land on "1" and an equal chance to land on anything else. Since there's a 40% chance to land on "1", this leaves 100% - 40% = 60% for everything else.
Let's define two events
A = event of landing on "1".B = event of landing on anything else (2 through 6).So far we know that P(A) = 0.40 and P(B) = 0.60; I'm using the decimal form of each percentage.
The net value of event A, which I'll denote as V(A), is -100 since you pay $100 when event A occurs. So we'll write V(A) = -100. Also, we know that V(B) = 30 and this value is positive because you receive $30 if event B occurs.
To recap things so far, we have the following:
P(A) = 0.40P(B) = 0.60V(A) = -100V(B) = 30Multiply the corresponding probability and net value items together
P(A)*V(A) = 0.40*(-100) = -40P(B)*V(B) = 0.60*30 = 18Then add up those products:
-40+18 = -22
This is the expected value, and it represents the average amount of money you earn for each dice roll. So you'll lose on average about $22. Because the expected value is not zero, this means this game is not mathematically fair.
This does not mean that any single die roll you would lose $22; instead it means that if you played the game say 1000 or 10,000 times, then averaging out the wins and losses will get you close to a loss of $22.
find the cost of fencing a rectangular field 250m long and 130m wide at rupees 30 per meter
Answer:
length of rectangular =250m
breath =130m
perimeter of rectangular field =(130*250)
=32500m
cost of fencing a rectangular field at the rate of 30 per meter
cost of the rectangular field =32500*30
=rupees 975000
hope it helps
A random sample of 900 13- to 17-year-olds found that 411 had a computer in their room with Internet access. Let p be the proportion of all teens in this age range who have a computer in their room with Internet access.Suppose you wished to see if the majority of teens in this age range have a computer in their room with Internet access. To do this, you test the hypotheses
H0: p = 0.50 vs HA : p≠0.50
The test statistic for this test is:_______.
a. 1.96
b. 2.60
c. 27.50
d. 2.59424
Answer:
The test statistic for this test is: z = -2.60, option b.
Step-by-step explanation:
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
H0: p = 0.50 vs HA : p≠0.50
This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5[/tex]
A random sample of 900 13- to 17-year-olds found that 411 had a computer in their room with Internet access.
This means that [tex]n = 900, X = \frac{411}{900} = 0.4567[/tex]
Value of the test-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.4567 - 0.5}{\frac{0.5}{\sqrt{900}}}[/tex]
[tex]z = -2.598[/tex]
The test statistic for this test is: z = -2.60, option b(should be).
3/10 of the beads in a jar are red, the rest are blue if there are 500 more blue beads than red, how many beads are together?
Answer:hope it helps.
Step-by-step explanation:
A car park has 20 vehicles 12 of them are cars.what fraction of the vehicles are cars?