You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.
From a random sample of 74 dates, the mean record high daily temperature in a certain city has a mean of 85.22 degrees F. Assume the population standard deviation is 13.97 degrees F.
Answer:
Very confused! at 95% confidence level, the true population mean will be between 134.33 and 145.67.
Step-by-step explanation:
A random sample of 45 home theater systems has a mean price of $140.00
Assume the population standard deviation is $19.40
population standard deviation is 19.40
sample size is 45.
standard error of the sample mean is 19.40 / sqrt(45) = 2.89198
at 90% confidence level, critical z is plus or minus 1.645.
at 95% confidence level, critical z is plus or minus 1.96.
critical raw score will be sample mean plus or minus critical z-score * standard error of the mean.
your sample mean is 140.
your standard error of the mean is 2.89198
at 90% confidence level, your critical raw score will be 140 plus or minus 1.645 * 2.89198.
that becomes 140 plus or minus 4.76 rounded to the nearest penny.
at 90% confidence level, the true population mean will be between 135.24 and 144.76.
at 95% confidence level, your critical raw score will be 140 plus or minus 1.96 * 2.89198.
that becomes 140 plus or minus 5.67 rounded to the nearest penny.
Using the z-distribution, it is found that:
The 90% confidence interval for the population mean is (82.55, 87.89). It means that we are 90% sure that the true population mean is between these two values.The 95% confidence interval for the population mean is (82.04, 88.40). It means that we are 95% sure that the true population mean is between these two values.The higher the confidence level, the higher the critical value is, and thus, a higher confidence level leads to a wider interval.We are given the standard deviation for the population, and thus, the z-distribution is used.
The information is:
Sample mean of [tex]\overline{x} = 85.22[/tex].Population standard deviation of [tex]\sigma = 13.97[/tex].Sample size of 74, thus [tex]n = 74[/tex].A z-confidence interval is given by:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
We have to find the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.
For the 90% confidence interval, [tex]\alpha = 0.9[/tex], thus, z with a p-value of [tex]\frac{1 + 0.9}{2} = 0.95[/tex], which means that it is z = 1.645.
Then, the 90% confidence interval is:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 85.22 - 1.645\frac{13.97}{\sqrt{74}} = 82.55[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 85.22 + 1.645\frac{13.97}{\sqrt{74}} = 87.89[/tex]
The 90% confidence interval for the population mean is (82.55, 87.89). It means that we are 90% sure that the true population mean is between these two values.
For the 95% confidence interval, [tex]\alpha = 0.95[/tex], thus, z with a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], which means that it is z = 1.96.
Then, the 95% confidence interval is:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 85.22 - 1.96\frac{13.97}{\sqrt{74}} = 82.04[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 85.22 + 1.96\frac{13.97}{\sqrt{74}} = 88.40[/tex]
The 95% confidence interval for the population mean is (82.04, 88.40). It means that we are 95% sure that the true population mean is between these two values.
The higher the confidence level, the higher the critical value is, and thus, a higher confidence level leads to a wider interval.
A similar problem is given at https://brainly.com/question/22596713
Which two ratios show a proportional relationship?
A. 2/8 and 6/20
B. 4/6 and 15/20
C. 10/15 and 12/18
D. 15/18 and 20/25
The Perimeter of a triangle is 90 cm. The triangle has side lengths of 2x + 5, 4x - 10, and x + 4. Find the value of x and the length of each side.
Answer:
I don't understand oof oof
Step-by-step explanation:
114 = 3x +18 what is the missing vaule
Answer:
x=32
Step-by-step explanation:
Hope this helps. Have a great day and plz give brainliest.
Eqiuvelent Ratio for 23:37
Solve the following equation and determine if it has one solution, no solution, or infinitely many solutions: 3x+1−3(x−1)=4
Answer:
1/3 , only one solution
Step-by-step explanation:
3x-1 = 1-3x
3x-1 = -3x+1
6x-1 = 1
6x = 2
x = 1/3
Answer:
Infinitely many solutions.
Step-by-step explanation:
[tex]3x+1-3(x-1)=4\\\\3x+1-1-3(x-1)=4-1\\\\3x-3(x-1)=3\\\\3x-3x-3=3\\\\\boxed{3=3}[/tex]
Hope this helps.
Solve for value of E
Answer:
4e +5+21=90
4e+26=90
4e=64
e= 16
Step-by-step explanation:
This is a 90 degree angle (right angle), soo you the measures given would be equal to 90 degrees
1.first simplify the equation
2. subtract 26 from both sides
3. Now divide 4 from boht sides to leave the unknown variable alone
4. You are left with the answer, which is 16
I hope this helps!
How do you do this question?
Answer:
[tex]\left \{ {{x=2+3\cos t} \atop {y\:=-1+3\sin t}} \right. => \pi \leq t \leq 5\pi[/tex]
Step-by-step explanation:
The standard equation of a circle centered at (a,b) with radius r would be (x - a)^2 + (y - a)^2 = r^2
This example represents a circle with center (2, - 1) having a radius of 3
The parametric equation of a circle centered at (0,0) would be;
x = r cos t,
y = r sin t
And so when centered at (a, b) we would have;
x = a + r cos t,
y = b + r sin t
In this case x = 2 + 3 cos t, and y = - 1 + 3 cos t
Now if the particle starts at (-1, - 1), correspondent to a start parameter of t = π, we need two revolutions so it should be that t = π + 2 * 2π = 5π.
[tex]\left \{ {{x=2+3\cos t} \atop {y\:=-1+3\sin t}} \right. => \pi \leq t \leq 5\pi[/tex]
what is 2819 divided by 55
Answer:
51.2545454545
Step-by-step explanation:
Answer:
51.25....
Step-by-step explanation:
Find the exact length of the third side. 2 4
Answer:
There isn't enough information on this question
Step-by-step explanation:
please answer my question
Answer:
hope that will help youIf a - 3 = 3^2/3 + 3^1/3, find the value of a^3 - 9a^2 + 18a.
Answer:
a(a-6)(a-3)
Step-by-step explanation:
3/4-1/12 subtract and simplify
Answer:
2/3
Step-by-step explanation:
Simplify the following:
3/4 - 1/12
Put 3/4 - 1/12 over the common denominator 12. 3/4 - 1/12 = (3×3)/12 - 1/12:
(3×3)/12 - 1/12
3×3 = 9:
9/12 - 1/12
9/12 - 1/12 = (9 - 1)/12:
(9 - 1)/12
9 - 1 = 8:
8/12
The gcd of 8 and 12 is 4, so 8/12 = (4×2)/(4×3) = 4/4×2/3 = 2/3:
Answer: 2/3
On Day 16 (in Segment 5), Ebony deposited $100 into her account. On each day after Day 16 (Segment 6) Ebony made a deposit, and those deposits were equal to each other.
(a) Explain how you can determine, just by looking at the graph, whether the amounts she deposited after Day 16 were each less than, equal to, or greater than $100.
(b) Use the graph to estimate B(21) in hundreds. Explain how you determined this estimate. Then, show how you can estimate the amount of money Ebony deposited into her account each day after Day 16.
Answer:
A)
Less than $100
B)
[tex]B(21)=300[/tex]
For each day after Day 16, Ebony deposited $40.
Step-by-step explanation:
We know that on Day 16 she deposited $100 into her account.
And each day after Day 16, she made a deposit and each deposit were equal to each other.
So, let's answer each of the questions using the available information.
Part A)
Notice that the 5th Segment starts and ends with the 5th to the 6th Point. The 6th Point represents the 16th Day, where B(16)=100.
We want to know whether or not each of her deposits after Day 16 were less than, equal to, or greater than $100.
We can immediately conclude that it must be less than $100 because we can see that the slope of the 6th Segment is less steep than the slope of the 5th Segment.
Since it is less steep, this means that the unit rate of change from each day after Day 16 is less than the unit change on Day 16, which is $100/day.
So, the each of the deposits made after Day 16 is less than $100.
Part B)
We want to estimate B(21) in hundreds.
Remember that Ebony's maximum balance is $400.
Also, recall that the first point is $200.
B(21), the 7th Point, seems to be between the 2nd/3rd Point and the 1st Point.
So, it is reasonable to say that at the 21st Day, her account balance was (200+400)/2=600/2=$300.
We know that at Day 16, her account balance was $100. So, we have the point (16, 100).
And at Day 21, her account balance is $300. So, (21, 300).
Since each deposit after Day 16 is the same, it has a constant rate of change. So, we can use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let (16, 100) be (x₁, y₁) and let (21, 300) be (x₂, y₂). Substitute them into the slope formula. This yields:
[tex]m=\frac{300-100}{21-16}[/tex]
Subtract and divide. So:
[tex]m=\frac{\$200}{5\text{ days}}=\$40\text{/day}[/tex]
So, for each day after Day 16, Ebony deposited $40.
And we're done!
5
Which input value produces the same output value for
the two functions on the graph?
x = -1
x = 0
x = 1
x = 2
Answer:
x = 1
Step-by-step explanation:
Input values are x-values plotted on the x-axis, while output values are the y-values plotted on the y-axis.
The question is simply asking that, which value of x will give us the same y-value for the two functions graphed above.
The x value that will give us the same y-value for both functions is the point where the line of both functions intercept. At that point, when x = 1, y = 1, in both functions.
Therefore, the input value of x = 1, will give an output value of y = 1, for the two functions on the graph.
Guys I need help I'm giving brainlist also show your work for me please this is my last math problem help
Answer:
.
Step-by-step explanation:
Derik earns $10.00 per hour. He works 35 hours per week. How much will he earn in two weeks? If he spends $50, how much will Derik have left?
Answer:
650
Step-by-step explanation:
so the way I did this was by adding how much he works per week which is 35 per week. so he works 70 hours in 2 weeks. he earns 10 dollars per hour. so 10 times 70 you get 700 but he spends 50. so 700 minus 50. you get 650. he has 650 dollars left.
What is the simplified expression for the expression below?
4(X + 8) + 5(x - 3)
O 9x + 5
9x + 11
o
9x + 17
9x + 47
Answer:
9x+17
Step-by-step explanation:
I took the test
James is learning to type. At the end of the first month, James could type 9 words per minute. At the end of the second month of practice, James could type 18 words per minute. After another month of practice, James could type 27 words per minute. James continued to practice. At the end of five months, how many words could James type per minute?
Answer: The answer is 36. Hope you have a nice day.
There you go
A scientific calculator costs $3.50 today. I remember when they cost about $75. What is the percent decrease in the price of a scientific calculator?
In other words: The decrease in price is what percent of the original price?
% Decrease= (Decrease in price(New price-Old Price))/(Original Price(old price))×100
Answer:
A scientific calculator costs $3.50 today. I remember when they cost about $75. What is the percent decrease in the price of a scientific calculator?
In other words: The decrease in price is what percent of the original price?
% Decrease= (Decrease in price(New price-Old Price))/(Original Price(old price))×100
Which answer choice shows these three expressions in order from least to greatest?
Answer:
Option D.
Step-by-step explanation:
Convert each to a decimal.
pie + 8 = 11.14
5 and the square root of 20 = 22.36
10/ the square root of 3 = 5.77
Now put them in order from least to greatest.
10/ the square root of 3, pie + 8, 5 and the square root of 20.
Option D is your answer!
What doubles can you use to find 4+5
Answer:
5 + 4 = 9 is near the doubles 4 + 4 = 8 and 5 + 5 = 10, so either double could be used to find the sum of 5 + 4.
Step-by-step explanation:
Hope this helps leave a heart c:
21-28 please geometry
9514 1404 393
Answer:
21–24 and 28 are correctly marked
25: NEI; 26: ASA or LA; 27: SSS
Step-by-step explanation:
25: At least one side is required for showing congruence. In figure 25, only angles are shown congruent, so there is not enough information.
__
26: Two angles and the side between them are marked congruent. These triangles can be declared congruent by ASA. Considering they are right triangles, one could also invoke LA as the appropriate theorem.
__
27: The unmarked sides of the two outside triangles can be shown to be congruent by virtue of the fact they are opposite congruent angles in the middle triangle. Hence all three sides can be shown congruent for those outside triangles, and the SSS postulate can be invoked.
P -5, 1 R 4,4..find the slope
Answer:
The slope between (-5,1) and (4,4) is 1/3
Step-by-step explanation:
When you're given 2 points and you must find the slope between those 2 points, you can find the distance between the y values and the x values.
For example in this case, the distance in our first y value is 3. So we know that y is always above x so we have 3/x so far.
Next to find the x values you do the exact same, and we get a distance of 9 from -5 to +4.
Now we have 3/9 which should be simplified to 1/3. When plotting this point, you'll use the strategy Rise over Run or Rise/Run.
(Side Note: Y is always above X so we know the Rise must be Y and the X must be Run.)
Y/X = Rise/Run
Hope this helps! :)
Select the correct answer.
Which statement is true about the y-intercept of a quadratic function?
ОА.
A quadratic function can only have one y-intercept.
OB.
A quadratic function can have up to two y-intercepts.
O c.
The y-intercept is also called a zero of the function.
OD
The y-intercept is located at the point where the value of y is 0.
Step-by-step explanation:
this is the answer .it is right or not
peggy is p years old maggie is 1 year less than 1/4 of peggys age what is maggies age in terms of p
Answer:
1/2m+100
Step-by-step explanation:
HELP NEEDED ASAP. "ONLY ANSWER IF YOU KNOW THE ANSWER"
Solve the equation by completing the square.
x^2 + 10x= -81
Answer:
x =-5± 2i sqrt(14)
Step-by-step explanation:
x^2 + 10x= -81
Take the coefficient of x and divide by 2
10/2 = 5
Square it
5^2 =25
add to each side
x^2 + 10x+25 = -81+25
( x+5) ^2 = -56
Take the square root of each side
sqrt(( x+5) ^2) =± sqrt(-56)
x+5 = ± sqrt(-1) sqrt(4*14)
x+5 =± i sqrt(4)sqrt(14)
x+5 =± i 2 sqrt(14)
Subtract 5 from each side
x+5-5 =-5± i 2 sqrt(14)
x =-5± 2i sqrt(14)
Anyone know how to evaluate this?
Ms. Smith has 132 stickers to give to her students. She has 25 students. If she gives the same number of stickers to each of her students, how many stickers will she have left over? *
Answer: 7
To find the remaining amount, we must multiply up to 132.
25 x 5 = 125
Subtract 125 from 132.
132 - 125 = 7
Answer = 7
The number of stickers Ms. Smith has leftover is 7.
Ms. Smith has 132 stickers and 25 students. She gives each student the same number of stickers. In order to determine the number of stickers she would have left, the number of stickers each student got has to be determined first. The stickers each student got can be determined by dividing the total number of stickers by the total number of stickers.
Total number of stickers each student got = total number of stickers / total number of students
132 / 25 = 5 (to the nearest whole number).
The total number of stickers distributed.
5 x 25 = 125.
The total amount of stickers left = 132 - 125 = 7 stickers.
A similar question was answered here: https://brainly.com/question/20291097?referrer=searchResults
Rani is make rice pudding. She uses 3/4 cup of white rice for every 2 cups of milk. How many cups of rice does she need when she uses 3 cups of milk? Show your work.
Answer:
10
Step-by-step explanation: