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VMariaS [17]
3 years ago
9

Suppose that a manager is interested in estimating the average amount of money customers spend in her store. After sampling 36 t

ransactions at random, she found that the average amount spent was $ 41.15 . She then computed a 90 % confidence interval to be between $ 38.01 and $ 44.29 .
Mathematics
1 answer:
musickatia [10]3 years ago
8 0

Answer:

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

The 90% confidence interval for this case would be (38.01, 44.29) and is given.

The best interpretation for this case would be: We are 90% confident that the true average is between $ 38.01 and $ 44.29 .

And the best option would be:

The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29

Step-by-step explanation:

Assuming this complete question: Which statement gives a valid interpretation of the interval?

The store manager is 90% confident that the average amount spent by the 36 sampled customers is between S38.01 and $44.29.

There is a 90% chance that the mean amount spent by all customers is between S38.01 and $44.29.

There is a 90% chance that a randomly selected customer will spend between S38.01 and $44.29.

The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

The 90% confidence interval for this case would be (38.01, 44.29) and is given.

The best interpretation for this case would be: We are 90% confident that the true average is between $ 38.01 and $ 44.29 .

And the best option would be:

The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29

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Given rectangle QUAD, If DU = 5x - 4 and QP = 2x + 7, then find the length of DU.
ira [324]

Answer:

DU = 86

Step-by-step explanation:

Properties of a rectangle,

- Opposite sides are equal in measure.

- Diagonals of a rectangle are equal.

- Diagonals bisect each other.

In the given rectangle QUAD,

Diagonals AQ and DU bisect each other at P.

AQ = DU

2(QP) = DU [Since, AQ = 2(PQ)]

2(2x + 7) = 5x - 4

4x + 14 = 5x - 4

5x - 4x = 14 + 4

x = 18

Since, DU = 5x - 4

DU = 5(18) - 4

     = 90 - 4

     = 86

Therefore, measure of DU = 86 units

3 0
3 years ago
One batch of fruit punch contains 1/3 quart grape juice and 1/5 quart apple juice. Colby makes 11 batches of fruit punch. How mu
zhuklara [117]

Answer:

3.66666666667

Step-by-step explanation:

If you multiply the number of batches he makes and the amount of grape juice he needs for every quart, you get and answer of 3.66666666667.

1/3 * 11= 3.66666666667

If you need to round the answer it would be 3.67

8 0
3 years ago
The value of U.S exports to China increased from $1480 million in 2011 to $2768 million in 2012. What was the percentage increas
loris [4]

Answer: Percentage increase is <em><u>87.02%.</u></em>

Explanation: Percentage increase is calculated by subtracting the value in 2012 from the value of exports in 2011 and then dividing it by the value in year 2011.

a. Subtract value in 2012 from value in 2011

b. Divide the answer in part a by value in 2011.

c. Multiply the answer in part b by 100.

We have the percentage increase.

<u>mark brainliest pls </u>

8 0
2 years ago
What does powers of fractions mean <br> we learned it today and i didn't get it
Leokris [45]
Its same as powers of a whole number.
Lets take example
(1/2)²=1/2×1/2=1/4
We can write it in a different way (0.5)²=0.5×0.5=0.25
4 0
3 years ago
What value of k makes the statement true?<br> x² (2x³ + 7x²yª) = 2xªyª + 7x³y8?
Nina [5.8K]

By apply the distributive property of multiplication, the value of k which makes the statement true is 1.

<h3>What is the distribution property?</h3>

Mathematically, the distributive property of multiplication is given by tis expression:

x(y + z) = xy + xz.

Next, we would apply the distributive property of multiplication to the given equation by distributing to the left-hand side using xy⁴:

k(2x⁴y⁴ + 7x³y⁸) = 2x⁴y⁴ + 7x³y⁸

Dividing both sides by the common factor, we have:

k = (2x⁴y⁴ + 7x³y⁸)/(2x⁴y⁴ + 7x³y⁸)

k = 1.

In conclusion, the value of k which makes the statement true is 1.

Read more on distributive property here; brainly.com/question/2807928

#SPJ1

<u>Complete Question:</u>

What value of k makes the statement true?

x^ky⁴(2x³ + 7x²y⁴) = 2x⁴y⁴ + 7x³y⁸

5 0
2 years ago
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