Mathematics College

A researcher is interested in finding a 95% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 150 students who averaged 42 minutes concentrating on their professor during the hour lecture. The standard deviation was 12 minutes.
Round your answers to two decimal places.
A. The sampling distribution follows a ____ distribution.
B. With 95% confidence the population mean minutes of concentration is between_____ and_____ minutes.
C. If many groups of 150 randomly selected students 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 minutes of concentration and about ______ percent will not contain the true population mean number of minutes of concentration.

Answers

Answer 1

Answer:

A. Normal

B. Between 40.08 minutes and 43.92 minutes.

C. About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.

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, a normal distribution.

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 - 0.95}{2} = 0.025[/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 - 0.025 = 0.975[/tex], so Z = 1.96.

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 = 1.96\frac{12}{\sqrt{150}} = 1.92[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.92 = 40.08 minutes

The upper end of the interval is the sample mean added to M. So it is 42 + 1.92 = 43.92 minutes

Between 40.08 minutes and 43.92 minutes.

Question C:

x% confidence interval -> x% will contain the true population mean, (100-x)% wont.

So, 95% confidence interval:

About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.

Related Questions

if the game begins at 1 pm and charlie and his friends take 1.5 hours to get to the field what time should they leave

Answers

Answer:

11:30am

Step-by-step explanation:

Answer:

Charlie and his friends should leave by 11:30 am at the latest.

Plz help this is due today AND NO LINKS OR GROSS PICTURES OR I REPORT

Answers

Answer:

90

Step-by-step explanation:

an obtuse angle is an angle from 90 - 180 degrees, so it would greater than 90 degrees

Which of the following sequences is an arithmetic sequence? Select all correct answers.
Select all that apply:

1,2,3,4,5,6,…
5,0,−5,−10,−5,0,…
−4,−6,−8,−10,−8,−6,…
3,0,−3,−6,−9,−12,…
6,5,4,3,2,1,…

Answers

Answer:

1st, 4th and 5th are in arithmetic sequence.

Answer:

a) 1,2,3,4,5,6............

d) 3,0, -3 ,-6,-9,-12.............

e) 6,5,4,3,2,1...........

are arithmetic sequence

Step-by-step explanation:

Arithmetic sequence is series of numbers that the difference of consecutive terms is constant

a) 1, 2 , 3 , 4 , 5 , 6...........

Common difference = 1

d) 3,0, -3 ,-6,-9,-12.............

Common difference = second term - first term

                                  = 0 - 3 = -3

e) 6,5,4,3,2,1...........

Common difference = 5 - 6 = - 1

Find the area of the shaded region

Answers

Answer:

Step-by-step explanation:

Area of the Shaded region = area of the Trapezoid - Area of the triangle

Area of the Trapezoid

b1 = 14

b2 = 26

h = 15

Area = (b1 + b2 ) * h / 2

Area = (14 + 26) * 15/2

Area = 40 * 15/2

Area = 300 in^2

Area of the triangle

Area = 1/2 b * h

b = 26

h = 15 - 6

h = 9

Area = 1/2 * 26 * 9

Area = 117 in^2

Area of the shaded region

Area of the shaded region = 300 - 117

Area of shaded region = 183

GIVING EVERYTHING IF CORRECT. NO fake answers, you will be reported. And it hurts my grades so please don't.

Answers

Answer is C, hopefully I helped. :)

23652.9/36
Maths decimals

Answers

Answer:

657.025 is the correct answer.

Answer:

657.025

Step-by-step explanation:

I did the math.

(2 * 15x) + (2 * 10)

Answers

Answer:

[tex](2 \times 15x) + (2 \times 10) \\ = 30x + 20 \\ = 10(3x + 2)[/tex]

Answer:

30x+20

Step-by-step explanation:

(2*15x) is 30x

(2*10) is 20

30x+20 can't be further simplified

The graph below shows which system of inequalities?

Answers

The answer you were looking for is

Convert 42°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas

c=5/9(F-32)
F=9/5 C+32

Answers

9514 1404 393

Answer:

  5.6 °C

Step-by-step explanation:

Put the number in the formula and do the arithmetic.

  C = 5/9(42 -32) = 5/9(10) = 50/9 = 5 5/9

  42 °F ≈ 5.6 °C

HELP PLEASEE HURRY PLEASE

Answers

Answer:

Here

Step-by-step explanation:

if one of the factor of x2 + x - 20 is (x+5).find the other.
a.x-4
b.x+2
c.x+4
d.x-2​

Answers

Answer:

a,x-4

hope it helps .....

Evaluate the expression when d= 75
2d + –45d = 0

Answers

Answer:

- 3225

Step-by-step explanation:

d = 75

2d + ( - 45 d )

= 2 ( 75 ) - 45 ( 75 )

= 150 - 3375

= - 3225

PLEASE ANSWER FAST! WILL GIVE BRAINLIEST

Answers

Answer:

B po

Step-by-step explanation:

Kase interquartile range po yan

This scale shows weight in pounds. How much do the apples weigh?



A. 3/4 lb.
B. 3 lb.
C. 3 1/4 lb.
D. 4 lb.

Answers

Answer:

where is the scale

Step-by-step explanation:

where is the scale

Answer:

What does the scale look like?

Suppose one serving of vegetables is 3/4 cup. How many servings there in 3 1/2 cups?

Explain your reasoning​

Answers

Answer:

14/3 or 4.6

Step-by-step explanation:

you would do 3.5 divided by .75 (=^w^=)

Check this out mate! Good luck

-5 = 1 / 3 ( -1 - w )
plz help with step by step answer

Answers

Step-by-step explanation:

[tex] - 5 = \frac{1}{3} ( - 1 - w) \\ \frac{1}{3} ( - 1 - w) = - 5 \\ - 1 - w = - 5 \div \frac{1}{3} \\ - 1 - w = - 5 \times 3 \\ - 1 - w = - 15 \\ - w = - 15 + 1 \\ - w = - 14 \\ w = 14[/tex]

1
If ZA and ZB are complementary angles and mA = 60°, then m B =?

Answers

Answer:

30 degrees

Step-by-step explanation:

Because the angles are complementary, they MUST equal to 90 degrees

Because measure of Angle A = 60, then the measure of Angle B = 30, because 60 + 30 = 90 degrees

Help! I’ll give brainliest it’s on quadratic equations

Answers

Answer:

divide b by 2 and square it to get c:

-20/2 = -10

[tex](-10)^2 = 100[/tex]

second part: (x - 10)(x - 10) or [tex](x-10)^2[/tex]

Answer:

x (x-20)

Step by step

A stainless steel patio heater is a square pyramid. The length of one side of the base is 24.8 in. The slant height of the pyramid is 89.3 in. What is the height of the pyramid?

Answers

Answer:

The height is  88.434in

Step-by-step explanation:

The number 312.8 is 34% of x. What is the value of x rounded to the nearest whole number

Answers

Answer:

X = 920

Step-by-step explanation:

To start off, we have to find how many times 34% can go into 100%. It can go in precisely 2.94117647059 times. Then, we take that number and multiply it by 312.8, since 312.8 is 34% of 100%. We get 920 from that, which is the answer.

Hope this helped!

A percentage is a way to describe a part of a whole. The value of x rounded to the nearest whole number is 920.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the number 312.8 is 34% of x. Therefore, we can write,

34% of x = 312.8

(34/100) × x = 312.8

Multiply both the sides of the equation by 100,

(34/100) × x × 100 = 312.8 × 100

Divide both the sides of the equation by 34,

[(34/100) × x × 100] ÷ 34 = (312.8 × 100) ÷ 38

x = (312.8 × 100)/34

x = 920

Hence, the value of x rounded to the nearest whole number is 920.

Learn more about Percentages here:

https://brainly.com/question/6972121

#SPJ2

which line has a slope of -1/2?
A.) line d
B.) line c
C.) line b
D.) line a

Answers

Answer:

C) line d

Step-by-step explanation:

Line D’s slope is -1/2, so C is the correct answer.

what is the volume for this figure please I will list brainliest I really need the answer​

Answers

Answer:

the answer is 708.75

Step-by-step explanation:

The country of Freedonia has decided to reduce its carbon dioxide emission by 3 5 %every year. This year the
country issued 40 million tons of carbon dioxide.

Answers

Answer:

Brainliest?

Step-by-step explanation:

The amount after t years 40 millions tons  

Bit by bit clarification:  

Given as :  

The pace of abatement of carbon dioxide one another = 35%  

The amount of carbon dioxide radiated for this present year = 40 million tons  

Let the amount of carbon dioxide discharged after t year = A millions tons  

Presently, According to address  

The amount of carbon dioxide radiated after t year = The amount of carbon dioxide discharged for this present year ×  

Or on the other hand, A millions tons = 40 millions tons ×  

Or on the other hand, A millions tons = 40 millions tons ×  

Or on the other hand, A millions tons = 40 millions tons ×  

Or on the other hand, A millions tons = 40 millions tons ×  

So,The amount after t years = A = 40 millions tons  

Consequently The amount after t years 40 million

What would 'x' be in the equation -3(x-2)=6?

Answers

Answer:

[tex]\boxed {\boxed {\sf x=0}}[/tex]

Step-by-step explanation:

To solve this equation, we must isolate the variable (x) using inverse operations.

[tex]-3(x-2)=6[/tex]

x-2 is being multiplied by -3. The inverse operation of multiplication is division, so we divide both sides by -3.

[tex]-3(x-2)/-3= 6/-3\\(x-2)=6 /-3 \\(x-2)= -2[/tex]

2 is being subtracted from x. The inverse operation of subtraction is addition, so add 2 to both sides of the equation.

[tex]x-2+2=-2+2\\x=-2+2\\x=0[/tex]

In this equation, x is equal to 0.

For the diagram below ,The Value of q , r is

Answers

Answer:

angle r= 45°

angle r+angle q=180°

45°+ angle q=180°[linear pair]

angle q=180°- 45°

angle q= 135°

If 40 is increased to 56, what is the percent of change?

80%
29%
40%
71%


​

Answers

The percent of change is 71%

Answer:

what the first person said

Step-by-step explanation:


Find the distance between (1, 2) and (5,5).

Answers

Answer:

The distance is 5 units

Step-by-step explanation:

Use the distance formula to find the distance.

The following equation is true for all real values of k for which the expression on the left is defined, and A
is a polynomial expression.
6k2 – 36k k2 + 12k + 36
А
k2 - 36
1
What is A?

Answers

Answer:

A = 6k(k + 6)

Step-by-step explanation:

We have to solve the given equation for the value of A,

[tex]\frac{6k^2-36k}{A}.\frac{k^2+12k+36}{k^2-36}=1[/tex]

[tex]\frac{(6k^2-36k)(k^2+12k+36)}{A(k^2-36)}=1[/tex]

(6k² - 36k)(k² + 12k + 36) = A(k² -36)

6k(k - 6)(k + 6)² = A(k - 6)(k + 6)

A = [tex]\frac{6k(k-6)(k+6)^2}{(k-6)(k+6)}[/tex]

A = 6k(k + 6)

Therefore, value of A is 6k(k + 6).

...
6
2.
Find the value of x in the parallelogram below.
33
16

Answers

Answer:

sorry where is the parallelogram

Answer:

your question is imcomplete

Step-by-step explanation:

Is the graph increasing, decreasing, or constant?
AY
8
2
4
B
8
A. Increasing
B. Constant
C. Decreasing

Answers

Answer:

there's no picture sorry I couldn't help

The answer is Increasing
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