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.

Answers

Answer 1

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.


Related Questions

Does anyone know what the answer please?

Answers

Answer:

[tex]\angle 1 \cong \angle 7[/tex]

Step-by-step explanation:

We proceed to present which angles corresponds with [tex]\angle 7[/tex], accompained with reason based on Theorems used in Euclidean Geometry. Two angles are correspondent if and only if are in the same side of the secant line, one of them is internal and the other one is external.

Hence, we conclude that [tex]\angle 1 \cong \angle 7[/tex].

please help im stuck on this question​

Answers

Answer:

(12,0)

Step-by-step explanation:

slope m=

[tex]\frac{54-36}{27-22} =\frac{18}{5}[/tex]

[tex]y-36=\frac{18}{5}(x-22)\\\\5y-180=18x-396\\\\y=\frac{18x}{5} -\frac{46}{5}[/tex]

[tex]0=\frac{10}{5}x-\frac{46}{5}\\\\x=\frac{216}{18} =12[/tex]

hope it helps...

have a great day

Jennifer made a baby blanket that is 2 feet by 3 feet. She has a queen size blanket that is 6 feet by 9 feet. How does the area of the baby's blank t compare to the size of the queen sized blanket?

Answers

The area of the baby blanket is 6 feet. The area of the queen size is 54 feet.
The area of the baby blanket is 9x smaller.

The area of the queen sized blanket is 9 times bigger than the area baby blanket.

What is the area of a rectangle?

The area of a rectangle is the multiplication of it's length and breadth.

Here, the area of the baby blanket = 2 × 3 square feet = 6 square feet.

The area of the queen sized blanket = 6 × 9 square feet = 54 square feet.

Therefore, the ratio of the baby blanket : queen sized blanket

= 6 : 54

= 1 : 9

Hence, area of the queen sized blanket is 9 times bigger than the area baby blanket.

Lear more about the area of the rectangle here: https://brainly.com/question/24408520

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y=-2
4x-3y=18
solve for x and y

Answers

No need to solve for y. The value of y is given. See it?

To find x, plug the given value of y into

4x - 3y = 18.

4x - 3(-2) = 18

4x + 6 = 18

4x = 18 - 6

4x = 12

x = 12/4

x = 3

Answer: y = -2 and x = 3.

Understand?

Answer:

X=3 y=-2

Step-by-step explanation:

4x-3y=18

4x-3(-2)=18

4x+6=18

4×=18-6

4x=12

divide both sides by 4

X=3

C = 172.7 cm
Use the formula, c = ad, and x = 3.14, to find the diameter of this circle whose circumference equals 172.7 cm.
A. 55 cm
B. 27.5 cm
O c. 542.278 cm
D. 5.5 cm
O E. 86.35 cm

Answers

Answer:

B

Step-by-step explanation:

number of bacteria in a certain population Increases according to a continuous exponential growth model with How many hours does it take the size of the sample to double ? growth rato parameter of 48% per hour

Answers

Answer:

It takes 1.77 hours for the population to double.

Step-by-step explanation:

Equation for population growth:

The equation for population growth, after t hours, with a growth rate parameter of r, as a decimal, is given by:

[tex]P(t) = P(0)(1+r)^t[/tex]

Growth rato parameter of 48% per hour

This means that [tex]r = 0.48[/tex]. So

[tex]P(t) = P(0)(1+r)^t[/tex]

[tex]P(t) = P(0)(1+0.48)^t[/tex]

[tex]P(t) = P(0)(1.48)^t[/tex]

How many hours does it take the size of the sample to double?

This is t for which P(t) = 2P(0). So

[tex]P(t) = P(0)(1.48)^t[/tex]

[tex]2P(0) = P(0)(1.48)^t[/tex]

[tex](1.48)^t = 2[/tex]

[tex]\log{(1.48)^t} = \log{2}[/tex]

[tex]t\log{1.48} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.48}}[/tex]

[tex]t = 1.77[/tex]

It takes 1.77 hours for the population to double.

5th grade math. correct answer will be marked brainliest

Answers

Answer:

7/12 teaspoons

fraction

Step-by-step explanation:

Amount of salt that would be used = 1[tex]\frac{3}{4}[/tex] x [tex]\frac{1}{3}[/tex]

Convert [tex]1\frac{3}{4}[/tex] to an improper fraction

to convert to improper fraction, take the following steps :  

1. Multiply the whole number  by the denominator

2. Add the numerator to the answer gotten in the previous step

3. divide the number gotten in the previous step by the denominator

(1 x 4) + 3 = [tex]\frac{7}{4}[/tex]

7/4 x 1/3 = 7/12

A coat cost $37.88 at Walmart. The sales tax is 5.5%. What is the total amount of the coat including the sales tax?​

Answers

$39.96 should be ur answer

what is the meaning of kiss

Answers

Answer:

wrong subject but, kiss means i guess to lock lips in a passionate way or in a greeting way. In some countries kissing someone on the cheek or past the cheek is a sign of a greeting i believe.

In short kissing means a way to show compassion or love.

Devon, Tony, and Nate were playing a board game. Devon wins when the spinner lands on green. Nate wins when the spinner lands on blue. Tony wins when the spinners lands on red. Which spinner should be used to make the game fair?

Answers

Answer:

c

Step-by-step explanation:

20POINTS! Determine if two triangles are congruent. If they are, state which theorem you can use to prove congruency. EXPLAIN WHY OR ELSE I WILL REPORT.

Answers

Answer:

both each side of each triangle is equal

use alphabets to mark each edge of the triangles and prove congruency

PLEASE HELP !! ILL GIVE BRAINLIEST !!

Answers

Answer:

Angles and XWY and STR

Step-by-step explanation:

These two angels are alternate exterior angels because:

- They are on different sides of the transversal (the line intersecting the two parallel lines)

- They have the same angle measure

- They are exterior, meaning they are on the outside, not inside (interior)

Hope this helps!!! :)

NEED ANSWER ASAP WILL GIVE BRAINLIEST FOR CORRECT ANSWER

Answers

Answer:

Slope

Step-by-step explanation:

Hope it helps you in your learning process

A quadrilateral is inscribed in a circle. Find the measure of each missing angle as labeled below. explain answer please

Answers

9514 1404 393

Answer:

C = 95°D = 72°F = 108°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary. Inscribed angles are half the measure of the arc they subtend. (The latter statement can be used to prove the former one.)

Using these relations, we have ...

  C = 180° -E = 180° -85° = 95°

  D = 144°/2 = 72°

  F = 180° -D = 180° -72° = 108°

Find the area of the figure. Round to the nearest tenth.
6.5
3
O 14.6 units2
O 22.4 units2
15.0 units2
O 18.2 units2

Answers

Answer:

Area total = 14.6

Step-by-step explanation:

The composite area from left to right is

a half circle plus a rectangle minus a triangle

Area total = π r²/2 + bh - 1/2(bh)

                = π (d/2)²/2 + bh - 1/2(b)(h triangle       use Pythagorean theorem

                = π (3/2)²/2 + 5(3) - 1/2(3)(√(3² - 1.5²)           h triangle = c² - (b/2)²

                = π 1.5²/2  + 15  -  1/2(3)(2.598)

Area total = 14.637 units²            

The number of miles that Kiki cycled each week for a 7-week period is shown:
36, 42, 28, 52, 48, 36, 31
What is the median number of miles Kiki cycled?

Answers

Answer:

36

Step-by-step explanation:

In this diagram use pythagoras theorem to calculate the length of the marked side

Answers

Answer:

[tex] 5\sqrt{7} [/tex]

Step-by-step explanation:

using Pythagoras theorem

[tex]d = \sqrt{ {20}^{2} - {(15)}^{2} } \\ [/tex]

[tex]d = 5 \sqrt{7} [/tex]

Step-by-step explanation:

Hyponues²= Base²+Height ²

20cm²=Base²+15cm²

400cm-225cm=H²

175=H²

5√7 Answer

What is the area of a square that has 2/4 units on each side

Answers

Answer:

1/4 of 0.25

Step-by-step explanation:

2/4 x 2/4 = 1/4

Between which values does 111 lie?
A. 7 and 8
B. 8 and 9
C. 9 and 10
D. 10 and 11
E .11 and 12

Answers

Answer: D: 10 and 11

Step-by-step explanation:

The Sq Rt of 111 is 10.5356537529 which falls between 10 and 11

Answer:

D: 10 and 11

Step-by-step explanation:

10.5356537529 10^11

and in standard notation:

105,356,537,529

Find the circumference of the circle and round to the nearest tenth

Answers

Answer:

circumference of circle = 2×pi×r

circumference of circle = 2×3.14×12.7

circumference of circle = 79.756 in

Please help, find the value of y

Answers

Answer

Step-by-step explanation:

chord makes  or arc make 120° at the center.

sum of other two angles of triangle=180-120=60

because they are equal.

so each angle=60/2=30°

tangent line makes angle 90° with radius .

so 30+y=90

y=90-30=60°

NEED NOW WILL NAME BRAINLYIST
Determine if the three side lengths given in each problem can create a triangle or not.
a. 12 cm, 14 cm, 20 cm
b. 4 m, 8 m, 12 m
c. 23 cm, 12 cm, 13 cm

Answers

Answer:

a) yes

b) no

c) yes

Step-by-step explanation:

the sum of the 2 shorter sides must be longer than the longest side

Answer:

a and c can make a triangle.

Step-by-step explanation:

the sum of 2 sides must be greater than the last side, all the way around. so 12+14 is better than 20. but 4+8 is not better than 12

There are 10 red apples and 12 green apples in a basket. If Vinta randomly selects 3 apples from
the basket, what is the probability they will all be green apples?

Answers

Answer: 1/7

Step-by-step explanation: 12/22 • 11/21 • 10/20

The probability they will all be green apples is 0.142 if there are 10 red apples and 12 green apples in a basket.

What is probability?

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

As we know,

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

It is given that:

There are 10 red apples and 12 green apples in a basket. If Vinta randomly selects 3 apples from the basket.

Total outcomes = number of ways of selecting fruits in the basket

Total fruits = 10 + 12 = 22

Total number of outcomes = C(22, 3) = 1540

Total number of favourable outcomes = C(12, 3) = 220

Probability = 220/1540

Probability = 0.142

Thus, the probability they will all be green apples is 0.142 if there are 10 red apples and 12 green apples in a basket.

Learn more about the probability here:

brainly.com/question/11234923

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T or F: If you consume more calories, you must decrease your physical activity to have energy
balance.
(not math but for pe)

Answers

Answer:

F

Step-by-step explanation:

When your losing weight after consuming more calories, you need to increase physical activity to increase the number of calories your body uses for energy.

T because if you consume more calories you will need to descrease ur physical activity

Find each measurement indicated. Round your answers to the nearest tenth.

Answers

Answer:

52.08°

Step-by-step explanation:

Law of sine: [tex]\frac{93}{25}[/tex]=[tex]\frac{x}{14}[/tex]

93*14=25x

1302=25x

52.08=x

A cone has a radius of 7 m and a height of 18 m . What is the approximate volume of the cone to the nearest tenth? Use 3.14 for pie

Answers

The answer is 923.2 because I found the circumference of the circle which was 153.86 and since it is the volume of the cone you would use the formula V=1\3BH. Using that formula you would do: 1/3*153.86(18) and that would get you 923.16 and since it looks like the answer wants you to round, you would get 923.2. Hope that helps!

Find the value of x in the isosceles triangle below then find the measure of the base angle.
x = __°
Measure of 1 base angle = __°

Answers

Answer: [tex]x=13[/tex], one base angle measures [tex]74^{\circ}[/tex]

Step-by-step explanation:

The base angles of an isosceles triangle are congruent, so:

5x + 9 = 8x - 30 [congruent angles have equal measure]9 = 3x - 30 [subtract 5x from both sides]39 = 3x [add 30 to both sides]x = 13 [divide both sides by 3]

Hence, the measure of one base angle is [tex]5(13)+9=\boxed{74^{\circ}}[/tex]

Help me pls I don’t get this one

Answers

Answer: <BAC is 28.5

Step-by-step explanation:

line AO and Line OB are congruent (both are radius of the circle)

<BAC and <OBA are congruent

<AOB is linear to BOC so 180-57= 123 <AOB is 123

Triangle AOB is Isosceles

2a+123=180

2a=57

a=28.5

I need to find the area!
Plz help me find the answer!

Answers

ANSWER:

680 sq units

MARK ME BRAINLIEST PLEASE

Weisen Sie bei folgenden Rechnungsbeträgen die Mehrwertsteuer aus!

a) 124,30 € b) 69,30 c) 12,50 €

Answers

Answer:

hj0

Step-by-step explanation:

Hi0 c cbdjdnsnsns d s
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