Mathematics College

Question 21 [t-interval] a random sample of size 18 is drawn from a population that is normally distributed. the sample mean is 58.5, and the sample standard deviation is found to be 11.5. determine a 95% confidence interval about population mean.
a. [52.78,64.22]
b. [53.78,63.22]
c. [53.18,63.81]
d. [54.04,62.96]

Answers

Answer 1

Answer:

Option a. [52.78,64.22]

Step-by-step explanation:

We are given that a random sample of size 18 is drawn from a population that is normally distributed.

Sample mean is 58.5, and the sample standard deviation is found to be 11.5 i.e., X bar = 58.5 and s = 11.5

The pivotal quantity for calculating 95% confidence interval is;

[tex]\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]

So, 95% confidence interval about population mean is given by;

P(-2.110 < [tex]t_1_7[/tex] < 2.110) = 0.95

P(-2.110 < [tex]\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.110) = 0.95

P(-2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] < [tex]{Xbar - \mu}[/tex] < 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ) = 0.95

P(X bar - 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] < [tex]\mu[/tex] < X bar + 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ) = 0.95

95% confidence interval about [tex]\mu[/tex] = [ X bar - 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] , X bar + 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ]

= [ 58.5 - 2.110 * [tex]\frac{11.5}{\sqrt{18} }[/tex] , 58.5 + 2.110 * [tex]\frac{11.5}{\sqrt{18} }[/tex] ]

= [ 52.78 , 64.22 ]

Therefore, 95% confidence interval about population mean is [52.78 , 64.22].

Related Questions

Each square is one square meter

Answers

36 square meters i believe

"you want to buy a new sports car from roy's cars for $51,800. the contract is in the form of a 48-month annuity due at a 9.2 percent apr. what will your monthly payment be"

Answers

the answer would be $1,284.13

Answer: $1,284.13

Step-by-step explanation:

As viewed from above, a swimming pool has the shape of the ellipse x24900+y22500=1, where x and y are measured in feet. the cross sections perpendicular to the x-axis are squares. find the total volume of the pool. v = cubic feet

Answers

4900>2500, the major axis of the ellipse is along x-axis
a=sqrt(4900)=70
b=sqrt2500=50

The squares are parallel to the y-axis, thus their sides extend in the y-axis direction, hence the length of the sides are:
y=+/-50sqrt(1-x^2/4900))
The area of the square
=y^2=[2500-2500(x^2/4900)

Thus, the volume will be sum along the x-axis from one of the ends of the ellipse to the other. by definition, the limits are (-a to a)=(-70 to 70)
But since the ellipse is symmetrical we can go from (0 to 70) and double the integral.
thus
V=2*int(0 to 70)[2500-2500(x^2/4900)]dx
=int(0 to 70)[5000-(50/49)x^2]dx
=[5000x-50/147x^3] (0 to 70)
=233,333 1/3 ft^3

One serving of Mike’s crackers has 150 calories and a mass of 30 grams. How many calories are in 6 grams of the crackers?

Answers

The amount of calories that are in 6 grams of crackers is 30 grams.

What is the amount of calories in the crackers?

Division is the mathematical operation that is used to determine the quotient of a number. It is the process of grouping a number into equal parts using another number.

Calories in 6 grams = (150 / 30) x 6 = 30 grams

To learn more about division, please check: https://brainly.com/question/13281206

#SPJ2

Final answer:

To find the calories in 6 grams of Mike's crackers, divide the total calories by the total mass of one serving to get the unit rate (5 calories/gram) and then multiply by the mass in question (6 grams) to obtain 30 calories.

Explanation:

The question asks how many calories are in 6 grams of Mike's crackers, given that one serving of 30 grams has 150 calories. To find the calories in 6 grams of the crackers, we can use unit rate and proportions.

Step-by-Step Calculation

First, determine the calories per gram of the crackers by dividing the total calories by the total mass (in grams) of one serving. This gives us the unit rate: 150 calories / 30 grams = 5 calories per gram.

Next, since we're asked about the calories in 6 grams, we multiply the calories per gram (unit rate) by the mass: 5 calories/gram × 6 grams = 30 calories.

Therefore, there are 30 calories in 6 grams of Mike's crackers. This calculation illustrates the utility of understanding proportions and unit rates in everyday applications such as determining caloric intake from portions of food.

the width of a rectangle is shown below:

Answers

The difference between the y-coordinates is 7 units. If the area is to be 42 square units, the missing coordinates must be 42/7 = 6 units to the right of those shown.
B = A +(6, 0) = (-4, 4) +(6, 0) = (-2, 4)

D = C +(6, 0) = (-4, -3) +(6, 0) = (-2, -3)

The appropriate choice is the last one, ...
(-2, 4) and (-2, -3)

There are 12 people having lunch.Each person wants 1/3 of a sub sandwich.How many whole sub sandwiches are needed ?use models to show answer.

Answers

12 people * (1/3 sandwich per person) = 4 sandwiches

3 and 2/3. 4 if the looking for a whole number

How do you evaluate this equation: a number decreased by the difference of m and 7? Please help and quick!!

Answers

Let n be the number.

A number decreased by the difference of m and 7 can be translated into mathematical expression as

[tex]n-\left(m-7\right)[/tex]

I have two bags. bag 1 contains 1010 blue marbles, while bag 2 contains 1515 blue marbles. i pick one of the bags at random, and throw 66 red marbles in it. then i shake the bag and choose 55 marbles (without replacement) at random from the bag. if there are exactly 22 red marbles among the 55 chosen marbles, what is the probability that i have chosen bag 1

Answers

55 blue or red marbles,

55-22 = 33 blue marbles

bag1+bag2= 2525

bag1=.4

33/55=.6 blue marbles

bag 2=.6

so it is 40% that U choose bag 1

a game has a deck of cards with 10 red cards, 4 blue cards, and 2 yellow cards. you randomly choose two cards(choose one and choose the second one without replacement) find the probability of choosing a blue card and a yellow card

Answers

[tex] \displaystyle
|\Omega|=\binom{16}{2}=\dfrac{16!}{2!14!}=\dfrac{15\cdot16}{2}=120\\
|A|=4\cdot2=8\\\\
P(A)=\dfrac{8}{120}=\dfrac{1}{15}\approx7\% [/tex]

is this correct if not help me

Answers

So far, so good.

You have properly counted squares and circles.

find the length of the side f .

Answers

I am pretty sure the answer is 10. Someone correct me if I'm wrong
[tex]10 {}^{2} + 15 {}^{2} = 18 {}^{2} \\ 100 + 225 = 325 \\ \sqrt{325} = 18 [/tex]

The length of side "f" would be about 9.95.

Using Pythagorean Theorem, you have the hypotenuse or side "c" (18) which is longest side. You also have side "b" (15).
Since the equation is "a^2 + b^2 = c^2”, fill in for "b" and "c" giving "a^2 + 15^2 = 18^2"
Solve for "a". Square each known value, leaving "a^2 + 225 = 324". Subtract 225 from each side, leaving "a^2 = 99" then use the square root on each side. Thus getting "a = 9.94987..., which rounded up is 9.95.

I hope this helps!

with an 18% discount, George was able to save 13.23 what was the original price

Answers

The original price is 74! Hope this helps!

18% = $13.23

1% = $13.25 ÷ 18 = $0.7361

100% = $0.7361 x 100 = $73.61

Answer: $73.61

Which graph best represents the equation -4x + 5y = 10?

Answers

Do you have a photo to show the separate graphs?

Answer: these are the graphs and i need the answer

Step-by-step explanation:

A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given: 50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 The following histogram is a representation of the data. Calculate the median ages

Answers

What you have to do to find the median of the data is first put that data into order numerically. You can go largest to smallest or smallest to largest, it doesn't matter.

22, 24, 28, 28, 30, 31, 31, 32, 32, 35, 36, 37, 38, 41, 42, 42, 44, 44, 45, 46, 46, 47, 47, 49, 50

Once you put them into order, you count towards the middle. You have 25 data points, so the middle, which will be your median number, will be 13 points in.

The median is 38

Final answer:

The median age of the sales representatives is 37.5 years.

Explanation:

To find the median ages of the sales representatives, we first need to order the ages in ascending order:

22 24 28 28 30 31 31 32 32 35 36 37 38 41 42 42 44 44 45 46 47 47 49 50 56

Since there are 25 data values, the middle value will be the median age. To find the middle value, we divide the number of data values by 2, which gives us 12.5. Since the median is the average of the two middle values, we can take the average of the 12th and 13th values in our ordered list:

Median age = (37 + 38) / 2 = 37.5 years

a piece of baseboard is 2/3 yard long. Angela cuts the board into pieces that are 1/6 yard long. How many pieces are there

Answers

namely, how many times does 1/6 go into 2/3, well

[tex]\bf \cfrac{\quad \frac{2}{3}\quad }{\frac{1}{6}}\implies \cfrac{2}{3}\cdot \cfrac{6}{1}\implies \cfrac{2}{1}\cdot \cfrac{2}{1}\implies 4[/tex]

if you flip a coin four times what is the probability of flipping tails four times

Answers

There are 16 possible outcomes.
Out of all 16 outcomes, there is only one way to get the result T T T T.
Therefore, the probability is 1/16 or 0.0625

hey can you please help me posted picture of question

Answers

The correct answer is the option B.To solve this problem you must apply the proccedure shown below:

1. You have the following expression:

(11-7i)-(16-11i)

2. If you want to substract both terms, you need to substract the real numbers and the complex numbers. Then, you obtain:

11-7i-16+11i
(11-16)+(-7+11)

3. Then, you obtain the following result:

-5+4i

4. Therefore, as you can see, the correct answer is the second option (option B), which is:

B. -5+4i

Correct answer is option B.

Solution is shown below:

To add or subtract two complex numbers, the real part is added or subtracted from real part and the complex part is added to or subtracted from complex part as shown below:

(11 - 7i) - (16 - 11i)

= 11 - 7i - 16 + 11i

= -5 + 4i

So, the answer to this question is option B

A listing of all possible outcomes of an experiment and their corresponding probability of occurrence is called

Answers

A listing of all possible outcomes of an experiment and their corresponding probability of occurrence is called Probability distribution

The listing of all possible outcomes for an experiment is known as a probability distribution.

The following information is related to the probability distribution is:

It is the table or an equation that is connected with each and every result of the statistical experiment along with the probability of occurrence.Also, it is the list of all possible experiment results.

Therefore we can conclude that the listing of all possible outcomes for an experiment is known as a probability distribution.

Learn more: brainly.com/question/22174871

HURRY PLEASE ITS TIMED
In the year 2000, Franklintown had a population of 30,000 people. Its population had decreased by 3% each year since then. Part A: Can this situation be modeled by an exponential decay function, an exponential growth function, or neither? Explain. Part B: If the population continues to decrease at the same rate, what would you expect the approximate population to be in 2016? Show your work.

Answers

Part A:
For this case we have a function of the form:
y = A * (b) ^ t
Where,
A: initial amount
b: decrease rate
t: time
Substituting values we have:
y = 30000 * (0.97) ^ t
Answer:
this situation can be modeled by an exponential decay function.

Part B:

We have the following function:
y = 30000 * (0.97) ^ t
For the year 2016 we have to:
t = 16
Substituting values:
y = 30000 * (0.97) ^ 16
y = 18427.6096
Rounding:
y = 18428
Answer:
The approximate population for 2016 is:
y = 18428

A soccer ball is kicked from the ground in an arc defined by the function, h(x) = -2x 2 + 8x. At what point does the ball hit the ground?

Answers

check the picture below. That's about what a parabola for an "initial velocity" case would look like.

anyhow, it hits the ground at two points, when it began, and when it came back down, and that happens when y = 0.

[tex]\bf h(x)=-2x^2+8x\implies \stackrel{h(x)}{0}=-2x^2+8x\implies 0=-2x(x-4)\\\\ -------------------------------\\\\ 0=-2x\implies 0=x\qquad \impliedby \textit{when it began}\\\\ -------------------------------\\\\ 0=x-4\implies \boxed{4=x}\qquad \impliedby \textit{when it came back down}[/tex]

Answer:

4 seconds

Step-by-step explanation:

h(t) = -3t^2 + 12t

0 = -3t^2 + 12t

0 = -3t(t - 4)

0 = t - 4

t = 4

Therefore, it takes 4 seconds for the rocket to hit the ground.

hope it helps :)

mark brainliest!

what is the area of a square with a radius of 9 cm

Answers

the answer would be 254.34

squares don’t have radius’, circles do. If you mean the length of one side is 9, then the area would be 81cm squared.

If you mean the area of a circle with a 9cm radius, then it would be 254.34 cm squared.

please help me with this if you can

Answers

The worst error will be where the prediction is farthest away from the actual value. Since the actual value corresponds to predictions in the 2nd column, the prediction at the far right (22.8) is the farthest away. The greatest error is ...
(22.8 -22.3)/22.3 * 100% ≈ 2.2%

What is the area of this figure?

Answers

As stated by @mathmate, the figure can be split into two rectangles (see picture). Then, we can find the total area by adding the areas of the individual rectangles. The area of the first rectangle is calculated by multiplying its length times width:

6 * 5 = 30

The area of the second rectangle is calculated by multiplying its length and width:

12 * 4 = 48

Now, we can add the areas to find the total area of the figure:

30 + 48 = 78

The figure's area is 78 cm².

What is the equation for the graph shown below?

Answers

Try this way:
the common view of the required equation is y=(x-a)(x-b), where 'a' and 'b' are the interception points (the curve and Ox).
using the coordinates of interception points it is possible to make up the required equation: x=3 and x=5.
y=(x-3)(x-5).
If to check the equation using the coordinates of the vertex (4;-1):
-1=(4-3)(4-5) ⇔ -1=-1, it means, that the equation made up is correct.

answer: y=(x-3)(x-5) or y=x²-8x+15.

hello can you please help me posted picture of question

Answers

B. Seven as your answer
:)

For this question we need to make a Venn Diagram as shown below.

Start from the inner most circle.

5 patrons like all 3 drinks.
8 patrons like Latte and Espresso. From these 8, 5 like all 3 drinks, so the patrons which only like Latte and Espresso will be 3.

Fill all the regions this way and you will get a diagram similar to the one given below.

Count all the numbers inside the circles. These add up to 47. This means 47 patrons like the drinks.

Total number of patrons was 50. So there are 7 such patrons which do not like any of these drinks.

So, the correct answer is option B

When subtracted, what is the simplified form of (5 − 3i) − (4 + 6i)? Write the answer in standard form, a + bi, where a and b are real numbers.

Answers

(5 - 3i) - (4 + 6i) Remove the brackets. Be careful with those on the right.
5 - 3i - 4 - 6i Did you notice how the second set worked. That - sign affected both terms inside the brackets. Now collect your like terms.

5 - 4 - 3i - 6i The - 3i and - 6i act like money. You are three dollars in the hold and you spend another 6. Where does that put you ?
1 - 9i You are now 9 dollars in the whole.

Suppose that 5 green balls and 12 purple balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn?

Answers

If the first ball is replaced and that we are not concern about the color of the first ball, then there is no concern for the first ball at all.

Total number of balls = 5 + 12 = 17
Total number of purple balls = 12

P(second one is purple) = 12/17

Answer: 12/17

Uisng the concept of probability, the probability that the second ball drawn is purple is 12/17

Given the Parameters :

Number of green balls = 5 Number of purple balls = 12

Total number of balls = 12 + 5 = 17

Recall :

Probability = required outcome / Total possible outcomes

Since selection is made with replacement :

P(purple) = number of purple balls / total number of balls

P(purple) = 12/17

Therefore, the probability of drawing a purple ball is 12/17

Learn more : https://brainly.com/question/18796573

in the plane figure shown below. if the degree measures of the angle are as shown, then x+y=

Answers

we know that

the sum of the internal angles in the figure shown is 360 degrees
so
360°=100°+60+70°+y+80°+x
360°=(x+y)+310°
(x+y)=360°-310°-----> 50°

the answer is
x+y is 50°

The amount of money that a student at harvard university carries on his/her person is normally distributed with a mean of $25 and a standard deviation of $15. what is the probability that a randomly selected sample of 25 harvard university students will have an average amount of less than $22 on his/her person?

Answers

Mean, m = $25
Standard deviation, s = $15
Sample size, n = 25 students
X <$22

Now,
Z = [(X - m)*Sqrt (n)]/s = [(22-25)*Sqrt(25)]/15 = -1

From Z tables,
P(X) = P(Z = -1) = 0.1587 = 15.87%

Therefore, probability that the selected sample has an average of less than $22 is 15.87%.

Under what circumstances is a t statistic used instead of a z score for a hypothesis test

Answers

If you know the population standard deviation sigma, then you'd use the z score. Otherwise, you would use a t statistic. However, if n is large enough (usually n > 30), then you can approximate the T distribution with the normal Z distribution. Some stats textbooks will allow the use of a z score if n > 30. Though it will depend on your specific book and/or your teacher.

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