A fashion designer wants to know how many new dresses women buy each year. A sample of 683 women was taken to study their purchasing habits. Construct the 95% confidence interval for the mean number of dresses purchased each year if the sample mean was found to be 4.6. Assume that the population standard deviation is 2. Round your answers to one decimal place.

Answers

Answer 1

The required confidence interval is (5.5<<5.7) for the mean number of dresses purchased each year.

As per the question, the given data as

[tex]\bar{x}[/tex] = 5.6

σ = 1.3

n = 650

The Z-critical value at the 95% confidence level is 1.960.

To determine the 99% confidence interval for the mean number of dresses purchased each year.

95% CI = [tex]\bar{x}[/tex]  ± Z(Cr)(s/√n)

⇒ -5.6 ± 1.960(1.3/√650)

⇒ 5.6±0.100

⇒ (5.500,5.700)

Round to near 1 decimal place

⇒ (5.5,5.7)

Therefore, the required confidence interval is (5.5<<5.7)

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Related Questions

How many meters are in a exameter?

Answers

Answer:

1E18 OR 10^18

Step-by-step explanation:

The formula is multiply the length by 1e+18

(1 point)
The number of eggs that a female house fly lays during her lifetime is normally distributed with mean 790 and standard deviation 92.
Random samples of size 98 are drawn from this population, and the mean of each sample is determined. What is the probability that
the mean number of eggs laid would differ from 790 by less than 30? Round your answer to four decimal places.

Answers

Answer:

0.9988 = 99.88% probability that the mean number of eggs laid would differ from 790 by less than 30.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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.

Mean 790 and standard deviation 92.

This means that [tex]\mu = 790, \sigma = 92[/tex]

Samples of 98

This means that [tex]n = 98, s = \frac{92}{\sqrt{98}}[/tex]

What is the probability that the mean number of eggs laid would differ from 790 by less than 30?

This is the pvalue of Z when X = 790 + 30 = 820 subtracted by the pvalue of Z when X = 790 - 30 = 760. So

X = 820

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{820 - 790}{\frac{92}{\sqrt{98}}}[/tex]

[tex]Z = 3.23[/tex]

[tex]Z = 3.23[/tex] has a pvalue of 0.9994

X = 760

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{760 - 790}{\frac{92}{\sqrt{98}}}[/tex]

[tex]Z = -3.23[/tex]

[tex]Z = -3.23[/tex] has a pvalue of 0.0006

0.9994 - 0.0006 = 0.9988

0.9988 = 99.88% probability that the mean number of eggs laid would differ from 790 by less than 30.

PLEASE HELP ME!!
For the following exercise, use the compound interest formula, A(t) = P(1 +r/n)^t.
where money is measured in dollars.
After a certain number of years, the value of an investment account is represented by the expression 10,400(1 +0.02/2)^20
had the account been accumulating interest?

How many years

Answers

Answer:

A = $10,441.68

A = P + I where

P (principal) = $10,400.00

I (interest) = $41.68

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 0.02/100

r = 0.0002 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 10,400.00(1 + 0.0002/2)(2)(20)

A = 10,400.00(1 + 0.0001)(40)

A = $10,441.68

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $10,400.00 at a rate of 0.02% per year compounded 2 times per year over 20 years is $10,441.68.

The total amount , with compound interest on a principal of $10,400.00 at a rate of 0.02% per year compounded 2 times per year over 20 years is $10,441.68.

What is Compound interest?

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest =[tex]P(1+r/n)^rt[/tex]

Given that

A = $10,441.68

A = P + I

P (principal) = $10,400.00

I (interest) = $41.68

First, we need to convert R as a percent to r as a decimal

r = R/100

r = 0.02/100

r = 0.0002 rate per year,

Then we will solve the equation for A

A = [tex]P(1+r/n)^rt[/tex]

[tex]A = 10,400.00(1 + 0.0002/2)^{(2)(20)}[/tex]

A = 10,400.00(1 + 0.0001)

A = $10,441.68

Hence, The total amount , with compound interest on a principal of $10,400.00 at a rate of 0.02% per year compounded 2 times per year over 20 years is $10,441.68.

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Find five rational numbers between 2/3 and 4/5

Answers

Answer:

Find five rational numbers between 2/3 and 4/5 -

61/90 62/90 63/90 64/90 65/90 66/90 67/90

choose any five :)

luego le digo 4yo1 xkw k ​

Answers

Answer:

okay luego le digo 4yo1 xkw k ​

Step-by-step explanation:

if $1000 is divided among the three people In the ratio 2:3:5,find the share of each​

Answers

Answer:

$200, $300, $500

Step-by-step explanation:

Given data

Total Amount= $1000

Ratio=  2:3:5

The combined ratio is = 10

Let us apply the part to all method to find the individual amount

The first person will take

10/1000= 2/x

1/100=2/x

cross multiply

x= 200

The second person will take

10/1000= 3/x

1/100=3/x

cross multiply

x= 300

The third person will take

10/1000= 5/x

1/100=5/x

cross multiply

x= 500

What is 4x minus x squared?

Answers

Answer:

3x^2

Step-by-step explanation:

the answer isssssssssssssssssssssssssss 3x^2.

In which quadrants is sine positive?
O A. I and IV
B. I and III
C. II and IV
D. I and II

Answers

Answer:

D. I and II

Step-by-step explanation:

In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive. 

The solution is, sine is positive in,  D. I and II. Option (D) is correct because, In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive.

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles.

here, we have,

We are given to select the correct answer from the options provided.

The rule of signs for the trigonometric ratios in the four quadrants are as follows :

Quadrant I :    All the three ratios, tangent, sine and cosine are positive.

Quadrant II :   Only sine is positive, cosine and tangent are negative.

Quadrant III :  Only tangent is positive, sine and cosine are negative.

Quadrant IV :  Only cosine is positive, sine and tangent are negative.

so, we get,

In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive.

Therefore, using the above rules, we can say that the options (B), (C) and (A) are incorrect.

so, we have,

Option (D) is correct because, In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive.

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Try to slove this question for me please

Answers

C. s is your answer.

The sum of 2 angles on a straight line (supplementary angles) is 180°. Vertical angles (opposites where a line intersects) are equal.

The upper left and lower right angles where p crosses the other lines (q, r, t) are 105°.

180 - 105 = 75°

So the upper right and lower left angles are 75°. The lower left angle where p intersects s is 85°, so it is not parallel to the others.

Please let me know if you have any questions.

I am really confused what a mean is in math

Answers

Answer:

A mean in math is when you have a set of numbers, you add up all numbers of the set and then divide that sum by the total amount of numbers.

Example: 3,6,8,9

3+6+8+9=26

26/4 (because there is four numbers)

26/4= 6.5

So the mean of that set will be 6.5

Step-by-step explanation:

solve for x in 2.3^x-81-3^x​

Answers

Answer:

===================

Solved by graphing: x =~ 3.711448

-----------

You can use a graphing calculator, or numerical

Can somebody please help me with this ?

Answers

Answer:

8x, 2x^2, 6xy, 5y.

Step-by-step explanation:

Hello, 5x+3x would be 8x since 5+3 is 8. 7x^2-5x^2 would be 2x^2 since 7-5 is 2 (exponents stay the same). 2xy+4xy is 6xy since 2+4 is 6. Lastly, 8y-3y is 5y since 8-3 is 5.

The diameter of a circle on
a coordinate plane has endpoints at (2,3) and (2,8) what is the approximate area of the circle

A. 16 units squared
B. 20 units squared
C. 25 units squared
D. 79 units squared

Answers

I’m pretty sure it’s c

Identify the 3D shape shown below. Choose 1 answer: A Cone B Cylinder с Rectangular prism​

Answers

Answer:

Cylinder

Step-by-step explanation:

Cones are pointed at the top or bottom

Rectangular Prisms are shaped like rectangles

Answer:

B

Step-by-step explanation:

Directions: Type your answer in the box below without using the ($) symbol.

Wesley had $792.38 in his checking account. He made the following transactions:
• He bought groceries at Food Lion using his debit card for $58.62.
• He received $50.00 for his birthday and deposited the money into his checking account.
• He made a withdrawal at the ATM from his checking account in the amount of $120.00. • He purchased a pair of shoes from the mall using his debit card in the amount of $64.98.
What was the final balance in his checking account after these transactions? ​

Answers

Answer:

Wesley's final balance in his checking account after these transactions is $598.78.

Step-by-step explanation:

792.38 - 58.62 + 50 - 120 - 64.98 = 598.78

Simply each answer .

Answers

Answer:

मुझे गर्म गले पसंद है

Step-by-step explanation:

Someone explain and help me do this for me I really need the help

Answers

Answer:

74.13

6×10=60

A=pi r^2

3.14×3^2=28.26

28.26/2 =14.13 (because it is half a circle)

14.13+60=74.13

not sure if that is correct but that is what i got

What is the mean of the set of data given below? 13 8 9 6 10 8​

Answers

Answer:

Mean = The numbers added up and divided by the number of numbers.

Step-by-step explanation:

= (13 + 8 + 9 + 6 + 10 + 8) / 6

= 54 / 6

= 9

The mean is 9.

Assume your home is assessed at $245,000. You have a $171,000 loan for 25 years at 6 percent. Your property tax rate is 1.4 percent of the assessed value. In year one, you would pay $10,260 in mortgage interest and $3,430 in property tax (1.4 percent on $245,000 assessed value).

Answers

Answer: $3,833.20

Step-by-step explanation:

Mortgages interest and property tax are both federal deductions so they will reduce taxes:

= 10,260 + 3,430

= $13,690

The tax saving is therefore:

= 13,690 * tax rate

= 13,690 * 28%

= $3,833.20

Which function is graphed below?



Answers

The answer for the question above is the B/Second one or

Y=3(1/3)^x

Help me I don’t know what this means

Answers

Answer:

46 is the 15th term.

Step-by-step explanation:

In this question they have given us the function 3x + 1 to determine the 15th term in the table. X =  the input or the numbers in that column. Now we must substitute x in our function to figure out the output.

Example:

3(1) + 1 = 4

So for the output for 1 the answer would be 4. You must follow this rule for 0 and 2 as well.

For 15 we must substitute 15 for x.

3(15) + 1 = 46

So 46 would be the 15th term.

Answer:

46

Step-by-step explanation:

[tex]3x+1[/tex]

To determine the 15th term using this expression, plug in 15 as x

[tex]= 3(15)+1\\= 45+1\\= 46[/tex]

Therefore, the 15th term is 46.

I hope this helps!

Can you help me please thank you

Answers

Answer:

-3ab, -9x^2 -13x

Step-by-step explanation:

45a^4b^3 - 90a^3b/ 15a^2b

-45ab^2/15a^2b

-3ab

13) (x-7x^2) - (2x^2+14x)

-9x^2 -13x

Hey guys!!! I forgot how to do this :/ lol
whats 10+4÷2?

Answers

Answer:

12

Step-by-step explanation:

The diagram shows the diameter of the opening
of a waffle ice cream cone.
18 cm
Which of the following is closest to the area of
the opening in square centimeters?
A.
1,017.88 cm2
C. 254.47 cm
B.
56.55 cm2
D. 28.27 cm2
I will give brainleist

Answers

Answers

D 36

Step-by-step explanation:

77 is the area for the squared trapezoid and 36 is the closest to 77

As you landscape a 4 leaf clover intersection, you will need to buy
enough grass seed to cover all 4 circles. Each of the circles has the same
diameter: 47 meters. Calculate the total area of all grass seed needed to
cover all 4 circles.

Answers

Answer:

A = 6940 m²

Step-by-step explanation:

We are told that there is a clover leaf intersection.

I have attached a picture of it with the 4 circles showing.

We are told the diameter of each circle is the same and equal to 47 m.

Thus, radius = 47/2 = 23.5 m

We want to find the area of grass that will cover the 4 circles. Thus;

Formula for area of a circle is;

A = πr²

For the 4 circles, we have;

A = 4πr² = 4 × π × 23.5²

A = 6939.78 m²

Approximately A = 6940 m²

Let f(x)=x^2-6 and g(x)=7x
Please help thank you

Answers

You are adding both equations
Since plugging in x makes the equations stay the same, just add f(x) and g(x)
x^2 - 6 + 7x

Solution: x^2 + 7x - 6

In an experiment, corn height was measured and recorded every hour (h) from the
moment the corn broke the surface. Scientists determined Ġ = 1.75h +0.55
represents the rate of change of the corn. How many units high was the first
recorded measurement? A)0.55 B)0.00 C)1.75 D)2.30

Answers

Answer:

its A

Step-by-step explanation:

14ab5 - 2ab5 + 4b2 +b

Answers

3b*(20a+3)!!!!! hope this helped

Answer:

80ab + 9b

Step-by-step explanation:

Step 1: 14 x 5 + 2ab x 5 + 4b x 2 + b

Then......

Multiple the numbers: 14 x 5 = 70

Step 2: = 70ab + 2 x 5ab + 4 x 2b + b

Then......

Multiple the numbers: 2 x 5 = 10

Step 3: = 70ab + 10ab + 4 x 2b + b

Then......

Multiple the numbers: 4 x 2 = 8

Step 4: = 70 ab + 10ab + 8b + b

Then......

Add similar elements: 70ab + 10ab = 80ab

Step 5: = 80ab + 8b + b

Then......

Add similar elements: 8b + b = 96

80ab + 9b

( I HOPE THIS HELPED!)

Combine like terms:
7x + 3x + 4y - X+.5y

Answers

Answer:

9x + 4.5y if .5y is a decimal point, 9x + 9y if the dot is a typo

Step-by-step explanation:

If the dot is real,

7x + 3x + 4y - x + 0.5y

10x + 4y - x + 0.5y

10x - x + 4y + 0.5y

9x + 4.5y

If the dot is a typo,

7x + 3y + 4x - x + 5y

10x + 4y - x + 5y

10x - x + 4y + 5y

9x + 9y

Answer:

the answer is 9x + 9y

7x + 3x + 4y - x + 5y

7x + 3x - x + 4y + 5y

10x - x + 4y + 5y

9x + 9y

i will be sooooo thankful if u helped me

Answers

the answer to question 35 is d

Answer:

For 35 its C

Step-by-step explanation:

 

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