Assume that a sample is used to estimate a population mean . Find the 99% confidence intervat for a Sample of size 68 with a mean of 65.9 and a standard deviation of 16.5. Enter your answer as an open- interval (low, high)

Answers

Answer 1

The 99% confidence interval for the population mean based on the given sample is (61.86, 69.94). This means that we are 99% confident that the true population mean falls within this interval.

To find the 99% confidence interval for a sample with a sample size of 68, a sample mean of 65.9, and a standard deviation of 16.5, we can use the formula for calculating the confidence interval for a population mean when the population standard deviation is known.

The formula is given by:

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / sqrt(sample size))

First, we need to find the critical value corresponding to a 99% confidence level. Since the sample size is large (n = 68), we can use the Z-table or a Z-table calculator to find the critical value. For a 99% confidence level, the critical value is approximately 2.576.

Next, we can substitute the given values into the formula to calculate the confidence interval:

Confidence Interval = 65.9 ± 2.576 * (16.5 / sqrt(68))

Using a calculator or mathematical software, we can calculate the standard error of the mean:

Standard Error = standard deviation / sqrt(sample size) = 16.5 / sqrt(68) ≈ 1.997

Substituting the standard error into the formula, we have:

Confidence Interval = 65.9 ± 2.576 * 1.997

Calculating the values inside the interval, we get:

Confidence Interval = (65.9 - 2.576 * 1.997, 65.9 + 2.576 * 1.997)

Simplifying further, we have:

Confidence Interval = (61.86, 69.94)

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Related Questions

Find the length of side x in simplest radical form with a rational denominator.

Answers

Answer:

since it is Right angled isosceles triangle it's base side are equal

by using Pythagoras law

x²+x²=1²

2x²=1

x=√{1/2}or 0.707 or 0.71

PLEASE HELP THIS IS TIMED!!

Answers

Answer:

(D) 3/10

Step-by-step explanation:

So its split into 10 different rates each and its on the third split So 3/10.

Can anyone help find x?

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Answer:

119

Step-by-step explanation:

Answer:

x= 61

Step-by-step explanation:

i think

6th grade math help me pleaseeee

Answers

Answer:

3 CDs

Step-by-step explanation:

If we have $65 and buy a $23 DVD, we will have $42 left.

So how many $14 CDs can we buy with $42?

All we have to do is divide 42 into 14, so we know how many groups of $14 we can make with $42.

42 ÷ 14 = 3

Therefore, Michella can purchase 3 CDs.

PLEASE HELP FAST WILL GIVE BRAINLIEST

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Answer:

The answer is 25 degree because there is ( 8x-1)

Multiply and combine like terms. Use^ for exponents. (3x+1)(2x^2 -9x+5)

Answers

Answer:

[tex]6x^{3} -25x^{2} +6x+5[/tex]

Step-by-step explanation:

PLEASE HELP I HAVE 5 MINUTES TO DO THIS AND I HAVE NO CLUE HOW
WILL MARK BRAINLIEST!!

Answers

A
B
C
A
. I think I wish you the best

Find the perimeter of the triangle.
A) 20
B) 51
C) 12 + 74
D) 12 + 47

Answers

D i know i’ve done it
The answer of the question is D

HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP

Answers

Answer:

B

Step-by-step explanation:

Sarah's house is not shown in graph

sketch the strophoid shown below. r = sec() − 2 cos(), − 2 < < 2

Answers

The strophoid is a curve represented by the polar equation r = sec(θ) − 2cos(θ), where -2 < θ < 2. In Cartesian coordinates, the strophoid equation can be written as (x^2 + y^2)^2 = 4y^2(x + 2).

The strophoid has a unique shape characterized by its looped structure.

The strophoid is symmetric with respect to the y-axis, as changing θ to -θ gives the same value of r. It has two branches that intersect at the origin (0, 0). As θ increases from -2 to 2, the curve starts from the rightmost point of the loop, extends to the left, and then returns back to the rightmost point.

The loop of the strophoid is created by the interplay of the secant function, which stretches the curve away from the origin, and the cosine function, which pulls it towards the origin. The strophoid exhibits interesting geometric properties and is often used in mathematical modeling and visualization.

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Mohammed is x years old.
Holly is 3 years older than Mohamed.
Karen is twice as old as Mohamed.
The total of their ages is 51.
How old is Mohamed?

Answers

Step-by-step explanation:

Mohammed age = x

Holly age = x + 3

Karen age = 2x

given,

[tex]x + (x + 3) + 2x = 51 \\ x + x + 3 + 2x = 51 \\ 4x + 3 = 51 \\ 4x = 51 - 3 \\ 4x = 48 \\ x = 48 \div 4 \\ = 12[/tex]

A faraway planet is populated by creatures called Jolos. All Jolos are either
green or purple and either one-headed or two-headed.
Balan, who lives on this planet, does a survey and finds that her colony of 500
contains 100 green, one-headed Jolos: 125 purple, two-headed Jolos; and
270 one headed Jolos.

Answers

Answer:

Option B

Step-by-step explanation:

We have to complete the table given in the question,

                         One headed               Two headed                    Total

Green                      100                       230 - 125 = 105        105 + 100 = 205

Purple            270 - 100 = 170                    125                      170 + 125 = 295

Total                         270                      500 - 270 = 230                500

By analyzing the given table,

Number of green Jolos in Balan's colony = Total of one headed green Jolos and Two headed green Jolos

= 205

Therefore, number of green Jolos in Balan's colony are 205.

Option B will be answer.

Answer:

When you put together the whole chart you will see the total is 205.

For every six dollars that Jamal saves in his account, his brother saves eight dollars in his account.

If Jamal has $24.00 dollars in his account, how much money does his brother have in his account?

Answers

Answer:

jamel brother has 48.00 dollors

Step-by-step explanation:

Answer: He has 32$ 24 divided by 6 is 4 multiply 4 by 8 and you get 32

cos80°.cos10°-sin80°.sin10°​

Answers

Step-by-step explanation:

The answer will be zero

here are the steps:

cos(90-10)xcos(90-80)-sin(90-10)xsin(90-10)=

(cos10xcos10)-(sin80xsin80)=

0.965111-0.965111=0

have a good day :)

I hope it will benefit you.

Factor 2x^2 - 3x = 2x - 2............Please?

Answers

Answer:

X = 1/2, 2

Step-by-step explanation:

= (2x-1)(x-2)

Answer:

OK I DON'T KNOW IF THIS IS IT BUT THE ANSWER IS POSSIBLY 0??? AND IF I DOESN'T WORK I'M SORRY

Step-by-step explanation:

I just need the answer if you don’t have a real answer but want to say something just comment it

Answers

Answer:

80??

Step-by-step explanation:


A sequence , satisfies the recurrence relation with
initial
conditions and . Find an explicit formula for the sequence.
+ k2 3) A sequence a,,a,,a z ..., satisfies the recurrence relation ax = 2x-1 + 2ax-2 with initial conditions a, = 2 and a = 7. Find an explicit formula for the sequence.

Answers

The explicit formula for the sequence [tex]\(a_n\)[/tex] is:

[tex]\(a_n = \begin{cases} 4n + 3 & \text{if } n \text{ is even} \\ 4n - 2 & \text{if } n \text{ is odd} \end{cases}\)[/tex]

To find an explicit formula for the sequence [tex]\(a_n\)[/tex] that satisfies the recurrence relation [tex]\(a_n = 2n-1 + 2a_{n-2}\)[/tex] with initial conditions [tex]\(a_1 = 2\)[/tex] and [tex]\(a_2 = 7\)[/tex], we can proceed as follows:

First, let's examine the first few terms of the sequence:

[tex]\(a_1 = 2\)\\\(a_2 = 7\)\\\(a_3 = 2(3) - 1 + 2a_1 = 5 + 2(2) = 9\)\\\(a_4 = 2(4) - 1 + 2a_2 = 8 + 2(7) = 22\)\\\(a_5 = 2(5) - 1 + 2a_3 = 9 + 2(9) = 27\)\\[/tex]

We can observe that the even-indexed terms [tex]\(a_2, a_4, a_6, \ldots\)[/tex] are increasing by a factor of 2, while the odd-indexed terms [tex]\(a_1, a_3, a_5, \ldots\)[/tex] are increasing by a factor of 3. This pattern suggests that we can split the sequence into two separate sequences:

For even-indexed terms:

[tex]\(b_n = a_{2n}\)[/tex]

For odd-indexed terms:

[tex]\(c_n = a_{2n-1}\)[/tex]

Let's find explicit formulas for both [tex](\(b_n\))[/tex] and [tex](\(c_n\))[/tex]:

1. Even-indexed terms [tex](\(b_n\))[/tex]:

The recurrence relation becomes:

[tex]\(b_n = 2(2n) - 1 + 2b_{n-1}\)[/tex]

To simplify the formula, let's rewrite [tex]\(b_n\)[/tex] as [tex]\(b_{n+1}\)[/tex] (i.e., shifting the index by 1):

[tex]\(b_{n+1} = 2(2n + 2) - 1 + 2b_{n}\)[/tex]

Subtracting the two equations, we get:

[tex]\(b_{n+1} - b_n = 4\)[/tex]

This is a simple arithmetic progression with a common difference of 4. To find an explicit formula for [tex]\(b_n\)[/tex], we can use the formula for the nth term of an arithmetic progression:

[tex]\(b_n = b_1 + (n - 1) \cdot \text{{common difference}}\)[/tex]

Substituting [tex]\(b_1 = a_2 = 7\)[/tex] and the common difference of 4, we have:

[tex]\(b_n = 7 + (n - 1) \cdot 4 = 4n + 3\)[/tex]

2. Odd-indexed terms [tex](\(c_n\))[/tex]:

The recurrence relation becomes:

[tex]\(c_n = 2(2n-1) - 1 + 2c_{n-1}\)[/tex]

Similar to before, let's rewrite [tex]\(c_n\)[/tex] as [tex]\(c_{n+1}\)[/tex]:

[tex]\(c_{n+1} = 2(2n + 1) - 1 + 2c_{n}\)[/tex]

Subtracting the two equations, we get:

[tex]\(c_{n+1} - c_n = 4\)[/tex]

Again, this is an arithmetic progression with a common difference of 4. Applying the formula for the nth term of an arithmetic progression:

[tex]\(c_n = c_1 + (n - 1) \cdot \text{{common difference}}\)[/tex]

Substituting [tex]\(c_1 = a_1 = 2\)[/tex] and the common difference of 4, we have:

[tex]\(c_n = 2 + (n - 1) \cdot 4 = 4n-2[/tex]

1) [tex]\cdot 4 = 4n - 2\)[/tex]

Now that we have explicit formulas for both [tex]\(b_n\)[/tex] and [tex]\(c_n\)[/tex], we can combine them to obtain the explicit formula for the original sequence [tex]\(a_n\)[/tex]:

For even-indexed terms, [tex]\(a_{2n} = b_n = 4n + 3\)[/tex]

For odd-indexed terms, [tex]\(a_{2n-1} = c_n = 4n - 2\)[/tex]

Therefore, the explicit formula for the sequence [tex]\(a_n\)[/tex] is:

[tex]\(a_n = \begin{cases} 4n + 3 & \text{if } n \text{ is even} \\ 4n - 2 & \text{if } n \text{ is odd} \end{cases}\)[/tex]

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Evaluate x-2 for x=-3

Answers

-3-2= -5

Put in -3 in x

Answer:

-5

Step-by-step explanation:

Rewrite x - 2 as -3 - 2, which comes out to -5.

Because of the Central Limit Theorem, the normal distribution is also a good approximation for the Poisson distribution. For a draw from a Poisson with parameter 1 = 37, what is the theoretical mean?

Answers

The theoretical mean for a draw from a Poisson distribution with parameter λ is equal to λ itself. In this case, λ = 37, so the theoretical mean is also 37.

Explanation:

The Poisson distribution is commonly used to model the number of events occurring within a fixed interval of time or space, when these events occur with a known average rate λ. The probability mass function of the Poisson distribution is given by P(X=k) = (e^(-λ) * λ^k) / k!, where X represents the random variable representing the number of events and k is the observed value.

The Central Limit Theorem states that when independent random variables are added, their sum tends toward a normal distribution, regardless of the shape of the original distribution. For a Poisson distribution, as the parameter λ increases, the distribution becomes more symmetric and bell-shaped, resembling a normal distribution.

Since the mean of a Poisson distribution is equal to its parameter λ, the theoretical mean for a draw from a Poisson distribution with parameter 1 = 37 is 37. This means that, on average, 37 events are expected to occur within the given interval.

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a is (4,15) and b is (8,1) what is the midpoint of AB?


Answers

Answer:

(6,8)

Step-by-step explanation:

midpoint=(x1+x2)÷2,(y1+y2)÷2

a(4,15) b(8,1)

x=4+8=12÷2=6

y=15+1=16÷2=8

Answer=(6,8)

Arrange the following fraction from least to greatest 2/3, 5/6, 3/5
What did you do to arrange the fraction from least to greatest?

Answers

Answer:

2/3 and 3/5 is same, then 5/6

Step-by-step explanation:

you can convert the fractions to decimals to find their value and then arrange them from least to the greatest.

Answer:

3/5, 2/3, 5/6 [From Least to Greatest]

Step-by-step explanation:

First you're going to want to know which one is "the bigger piece of pie".

I made a few drawing and look at the pictures (Just in case you have a different opinion from my answer)

PLEASE HELP IF I DONT PASS THIS TEST I FAIL AND I DON'T UNDERSTAND IT AND I AM ON THE VERGE OF MENTAL BREAKDOWN

Answers

Answer: One of the ways you can do all this is by zearn or by listening by your teacher.

Answer:

1 e

2 a

3 b

4 c

5 d

Step-by-step explanation:

i did the answers to the first question i dont know the rest sorry

Luis rolled a number cube 60 times. He rolled the number 6 four times. Which is most likely the cause of the discrepancy between Luis’s experimental outcome and the predicted outcome?

Answers

Luis isnt a fortune teller and shouldnt try to be one

HELP NO LINKS JUST ANSWER DUE TODAY

Answers

The value of x is 4.4

This is because to get from 10 to 4 you divide to get a scale image. 10 divided by 4 = 2.5. So to get the same scale length on the other side of the triangle you divide the side length of 11 by 2.5 which = 4.4
I hope this helps! Good luck on your homework!
4/10=x/11

0.4=x/11

x=0.4•11

x=4.4

6=2(y+2) i need help

Answers

Answer:

y=1

Step-by-step explanation:

6=2(y+2)

6=2y+4

2=2y

y=1

Answer:

y=1

Step-by-step explanation:

In order to check if blood pressure measurements change if one is sitting or standing, a study was conducted where systolic blood pressure of 35 patients were recorded while in sitting position and then again while standing. The comparison of systolic blood pressure in the two positions is an example of testing the difference between: a-Two means from independent populations b-Two population proportions c-Matched pairs from two dependent populations d-All of the above options are equally viable testing methods

Answers

The comparison of systolic blood pressure in the sitting and standing positions is an example of testing the difference between matched pairs from two dependent populations.

The scenario described involves measuring the systolic blood pressure of the same set of patients in two different positions (sitting and standing). This creates a dependency between the measurements because each patient serves as their own control. In this case, the appropriate statistical test would be a paired t-test or a related test for dependent samples.

Two means from independent populations: This option would be suitable if the measurements were taken from two different groups of patients who were independent of each other, but in this case, the same individuals were measured in both positions. Two population proportions: This option would be applicable if the data involved proportions or categorical variables, rather than continuous measurements like blood pressure.

Matched pairs from two dependent populations: This option accurately represents the scenario described, as the measurements were taken from the same individuals in both positions, making them dependent on each other.

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PLSS HELP IMMEDIATELY!!! i’ll give brainiest if u don’t leave a link!

Answers

D. Air Pockets in Their leaves

Those link sharing ppl are SOOOO annouing

Answer:

They have air-filled pockets in their leaves

Step-by-step explanation:

I need the length of DB and Measure of angle C in degrees!!!!!

Answers

Answer:

DB = 10

m∡C = 106°

Step-by-step explanation:

DE = EB

20x - 8 = 16x + 12

4x = 20

x = 5

DB = 5 doubled, or 10

m∡A + m∡D = 180

3y + 7 + 2y + 8 = 180

5y + 15 = 180

5y = 165

y = 33

m∡A = m∡C

m∡A = 3(33)+7 = 106°

m∡C = 106° also

Plz help ASAP !!!!! Plzzz

Answers

Answer:

The second one

Step-by-step explanation:

She started with x dollars and then used 8 dollars to buy a football game ticket, so x-8. Then, she is left with 56 dollars, so x-8=56. Therefore, the second story represents the equation.

If AABC = ADEC,
ZB = 44º and ZE = 4x
A
B
С
E
x = [?]

Answers

Answer:

The angle at B is the same as the angle at E so equate them to each other to find x

2x+4=40°

2x=40-4

2x=36

x=36/2=18

Step-by-step explanation:

Hope this is helpful! stay safe and God Bless:)))

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