A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 219 members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.9. Round answers to 3 decimal places where possible.
A. The sampling distribution follows a _______ distribution.
B. With 90% confidence the population mean number of visits per week is between _____ and ______ visits.
C. If many groups of 220 randomly selected members are studied, then a different confidence interval would be produced from each group. About ________ percent of these confidence intervals will contain the true population mean number of visits per week and about__________ percent will not contain the true population mean number of visits per week.
Answer:
A. Normal
B. Between 2.078 and 2.722 visits.
C. About 90 percent of these confidence intervals will contain the true population mean number of visits per week and about 10 percent will not contain the true population mean number of visits per week.
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]
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.
Question A:
By the Central Limit Theorem, normal.
Question B:
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 = 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.
[tex]M = 1.645\frac{2.9}{\sqrt{219}} = 0.322[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2.4 - 0.322 = 2.078 visits
The upper end of the interval is the sample mean added to M. So it is 2.4 + 0.322 = 2.722 visits.
Between 2.078 and 2.722 visits.
Question c:
90% confidence level, so 90% will contain the true population mean, 100 - 90 = 10% wont.
About 90 percent of these confidence intervals will contain the true population mean number of visits per week and about 10 percent will not contain the true population mean number of visits per week.
WHAT THE HECK IS THAT SHAPE PLEASE HELP IM SLOW
Answer: It looks like a Trapezoid
Step-by-step explanation:
Answer:
trapezoid
Step-by-step explanation
there are two lines across from each toher that are parallel, but the other two lines aren't , so this has to be a trapezoid. there are also no right angles
Substituting the equation x = 4y – 12 into the equation -2y = x – 6 will produce the equation _________.
Plz I need help with this
Answer:56
Step-by-step explanation:
Yuhhh please help ty :))
Answer:
20 oz.
Step-by-step explanation:
Hope this helps ! :)
I need the answer for this question
Answer:
6,912 i think that's the answer I'm not sure though
Step-by-step explanation:
Answer:
[tex]8,400in^2[/tex]
Step-by-step explanation:
Area of Trapezoid: [tex]A=h(\frac{b1+b2}{2} )[/tex]
Given: B1, B2 and h
B1 = 18 in
B2 = 24
h = 16 in
Substitute variables for the give numbers:
[tex]A=16(\frac{18+24}{2} )\\A = 336 in^2[/tex]
The 336 in is for one desk, and they want you to find 25 desks. So multiply 336 and 25.
[tex]x = 25(336)\\x = 8,400in^2[/tex]
Please help!!! Solve for the m
Answer:
36°
Step-by-step explanation:
[tex]m\angle C =sin^{-1}\frac{17}{29}\\m\angle C =35.888297553\degree\\m\angle C =36\degree[/tex]
Emilio’s truck has a gas tank that holds 25 gallons of gas and can travel 400 miles without refilling the gas tank. The graph below shows the amount of gas remaining in Emilio’s truck after he has driven a certain number of miles. Which of the following best describes a reasonable range for this situation
Answer:
[tex]Range: 0 \le y \le 400[/tex]
Step-by-step explanation:
Given
[tex]Gas = 25 gallons[/tex]
[tex]Distance = 400miles[/tex] --- max
Required
The range of the function
The graph is not given; however, the question can be answered without the graph.
From the question, we understand that the truck can hold up to 25 gallons.
This represents the domain (i.e. from 0 to 25)
When the truck is empty (i.e. no gas in it), the truck cannot move any distance (0 miles).
When the truck is filled up (i.e. 25 gallon), the truck can move up to 400 miles.
This represents the range (i.e. from 0 to 400 miles)
Hence, the range is:
[tex]Range: 0 \le y \le 400[/tex]
1) Determine the area of the shaded region.
14 ft
8 ft
Answer:
61.73 ft ^2
Step-by-step explanation:
area of rectangle
14x8 = 112
area of circle
π(4)(4) = 50.27
subtract
112-50.27 = 61.73
Find the amount due if $200 is borrowed for 10 months at an APR of 16% simple interest
Amount =?
Answer
$266.66
Step-by-step explanation:
We have here ,
Principal = $200 Rate = 16% Time = 10 months = 10/12 yrs.We can use the formula of SI to calculate the SI . After adding it to principal we will get the amount .
⇒ SI = P × R × T / 100
⇒ SI = $ 200 × 16 × 10 / 12 × 100
⇒ SI = $ 26.66
Now Calculate amount as ,
⇒ A = SI + P
⇒ A = $ 200 + $ 26.66
⇒ A = $ 226.66
An angle measures 60.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
the angles are 120.1 and 59.9
Step-by-step explanation:
supplementary means that the add up to be 180
I made a system of equations and to make thing faster I graphed them but if you wanted you could solve fully
x+y=180
y-60.2=x
10. Which of these is NOT a perfect square?
a. 81
b. 100
C. X2
d. 42
Answer: 42 is not a square of a whole number
Step-by-step explanation: 81= 9², 100= 10², x²= x·x, 6²= 36 and 7²= 49
what is the solution to 2(3m+4)=6(1-2m)
a) m=2
b) m=-2
c)m=-10
d.)m=1/5
Answer:
The answer is in the picture below.
Step-by-step explanation:
Given: Circle O; ZA intercepts BC; ZD intercepts BC Two statements are missing reasons. What reason can be used to justify both statements 2 and 3? Prove: ZA ZD Statements Reasons D 1. given A 1. circle O; ZA intercepts BC, ZD intercepts BC 2. m ZA= (MBC ) 3.m4D = 1mBC) (MBC 12.1? B 3.? 4. mZA=mZD 4. substitution property 5. ZASZD 5. definition of congruent angles O inscribed angles theorem
Answer:
A. Inscribed angle theorem
Step-by-step explanation:
The missing reasons in the proof are inscribed angles theorem.
What is an arc in a circle?In mathematics, an arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference.
Given that, a circle, with arcs AD and BC, we need to find the reason in the proof,
The reasons are inscribed angles theorem.
Inscribed angles theorem :-
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle.
Hence the missing reasons in the proof are inscribed angles theorem.
Learn more about arcs, click;
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y = x + 45
What is the y-intercept of the relationship?
A. 45
B. x + 45
C. x
D. y - 45
Answer:
D
Step-by-step explanation:
How come the tutors don't work??
Answer:
What do you mean? If you are talking about the Community not always answering Questions well that means your they don't know the right Answer
the Mods are Annoying and very skeptic of the Guidelines of Brainly.
Find the lengths of the legs.
(NO LINKS)
Given:
The figure of a right angle triangle with hypotenuse 10 and two angles [tex]45^\circ, 90^\circ[/tex]
To find:
The lengths of the legs.
Solution:
Two angles are given. By using the angle sum property, the third angle is:
Third angle = [tex]180^\circ-45^\circ- 90^\circ[/tex]
= [tex]45^\circ[/tex]
Base angles are equal it means the given triangle is an isosceles right triangle. So, the lengths of both legs are equal.
Let x be the lengths of both legs. Then by using Pythagoras theorem, we get
[tex]Hypotenuse^2=leg_1^2+leg_2^2[/tex]
[tex](10)^2=x^2+x^2[/tex]
[tex]100=2x^2[/tex]
[tex]\dfrac{100}{2}=x^2[/tex]
[tex]50=x^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{50}=x[/tex]
[tex]\pm 5\sqrt{2}=x[/tex]
[tex]\pm 5\sqrt{2}=x[/tex]
The side length cannot be negative. So, the only value of x is [tex]5\sqrt{2}[/tex].
Therefore, the length of the both legs is [tex]5\sqrt{2}[/tex] units.
Find the average of the function over the given interval. f(x) = x3 over [−1, 1]
9514 1404 393
Answer:
0
Step-by-step explanation:
f(x) = x^3 is an odd function, so is symmetrical about the origin. Its average value on any symmetrical interval around the origin will be 0.
The average value is 0.
What is the total surface area of the triangular prism shown?
Answer:
24 2/5ft
Step-by-step explanation:
add all the sides together.
4ft x 2
3ft x 2
10 2/5 x 1
=
24 2/5
Round to one billion place. Drop the zeros.
28,436,297,825
30,943,267,101
45,831,246,935
Answer:
28,436,297,825
30,943,267,101
45,000,000,000
Step-by-step explanation:
ur welcome
please help i don't understand this question
A the cost of buying the tablet
B the cost per month of internet service
C the number of months after wich the total cost is 0 dollars
D none of the above
Answer:
Pretty sure it would be b because it keeps scaling as the x axis continues with time
Need help on this question thanks
Answer:median
Step-by-step explanation: because median is used to be in the middle so those are numbers that would be in the middle, and if you add them up it would contain a high amount of number but if you subtract half you get your answer, and your Welcom!
Gretta is 1 1/2 meters tall. Which of the following is equivalent to 1 1/2 meters? A 150 millimeters B 1.500 millimeters C 100 millimeters D 1,000 millimeters
Answer:
1500 millimeters is your answer
Simplify 1 1/8 x 4 +2 5/6 x 3
Answer:
bro just search it on mathaway or calculator soup
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
A sprinkler rotates 360° to water a circular region. If the total area watered is approximately 2,200yd2, determine the radius of the region (the radius is length of the stream of water). Round the answer to the nearest yard.
Answer:
Radius = 26 yards.
Step-by-step explanation:
The complete rotation of the sprinkler makes a circle of radius R (R is the length of the stream of water).
Remember that the area of a circle of radius R is:
A = pi*R^2
where pi = 3.14
In this case, we know that the area is equal to 2,200 yd^2
Then:
A = 2,200 yd^2 = 3.14*R^2
Solving this equation we can find the value R.
(2,200 yd^2)/3.14 = R^2
√( (2,200 yd^2)/3.14) = R = 26.47 yards.
We want to round it to the nearest yard, then we need to look at the first digit after the decimal point. It is smaller than 5, then we round down, we get:
Radius = 26 yards.
X = {1,3,5,7)
Y = {13,57}
Which of the following is the set XnY?
Answer:x is a letter in music.} 3. Determine whether each set is well-defined. If it is not well-defined, explain why, ... true (e) {1, 3, 5, 7, 9) = {1, 5, 9, 3, 7) false_(f) {1,3,5, 9) = {1,3,5,9} ... Describe each of the following sets as either finite or infinite. ... 13 listened to heavy metal and alternative rock; 12 listened to rap and alternative rock;. or
x 2 - 2yZ = 7 with x = 2v + 1 and y = 2b + 1. These have solutions. (x, y; v, b) = (3, 1; 1,0), (5,3; 2,1), (13,9; 6,4),. (27,19; 13,9), (75,53; 37, 26), (157,111; 78, 55), .
Step-by-step explanation:
Find the mean of 9, 2, 2, 1, 1 graphically.
At the beginning of the month, Sarah had 600 in her bank account. Within the month she made two deposits of and She also made three withdrawals 100, , and 20. How much was in her account at the end of the month?
Answer:
At the end of the month she has $578
Step-by-step explanation:
Given
[tex]Start\ balance = 600[/tex]
[tex]Deposits=50; 100; 48[/tex]
[tex]Withdrawal: 100; 20; 100[/tex]
Required
The balance at month end
Deposits simply means adding cash to the account and it has a very simple interest. So, we add .
While Withdrawal taking money out of the account. So, we subtract.
So, we have:
[tex]Month\ end = Start\ balance + Deposits + Withdrawal[/tex]
[tex]Month\ end = 600 + [50 + 100 + 48] - [100 + 20 + 100])[/tex]
[tex]Month\ end = 600 + 198 - 220])[/tex]
[tex]Month\ end = 578[/tex]
Hence, at the end of the month she has $578
what is the domain of this exponential function , y=7^x
Answer: hope this helps
Step-by-step explanation:
Answer:
Hope this helped!!!
Step-by-step explanation:
Help!!!!!! Which function is best represented by this graph
Answer:j
Step-by-step explanation:
Answer:
J
Step-by-step explanation: