A researcher records the repair cost for 8 randomly selected refrigerators. A sample mean of $57.89 and standard deviation of $23.69 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer 1

Answer:

The question is incomplete! the complete question along with answer and step by step explanation is provided below.

Question:

A researcher records the repair cost for 8 randomly selected refrigerators. A sample mean of $57.89 and standard deviation of $23.69 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal.

Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 2 : Construct the 95% confidence interval. Round your answer to two decimal places.

Given Information:

Sample mean repair cost = $57.89

Sample standard deviation = σ = $23.69

Sample size = 8

Confidence level = 95%

Required Information:

step 1: critical value = ?

step 2: 95% confidence interval = ?

Answer:

step 1: critical value = 2.365

step 2: 95% confidence interval = ($38.08, $77.70)

Step-by-step explanation:

Since the sample size is less than 30 and the standard deviation of the population is also unknown therefore, we can use the t-distribution to find the required confidence interval.

The confidence interval is given by

$CI = \bar{x} \pm MoE\n\n$

Where $\bar{x}$ is the mean repair cost and MoE is the margin of error that is given by

$$ MoE = t_(\alpha/2)((s)/(√(n) ) ) $ \n\n$

Where n is the sample size, s is the sample standard deviation, and $t_(\alpha/2)$ is the t-score corresponding to 95% confidence level.

The t-score corresponding to 95% confidence level is

Significance level = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom (DoF) = n - 1 = 8 - 1 = 7

From the t-table at α = 0.025 and DoF = 7

t-score = 2.365

Therefore, the critical value that should be used in constructing the confidence interval is 2.365

$MoE = 2.365\cdot (23.69)/(√(8) ) \n\nMoE = 2.365\cdot 8.3756\n\nMoE = 19.808 \n\n$

So the required 95% confidence interval is

$CI = \bar{x} \pm MoE\n\nCI = 57.89 \pm 19.808\n\nCI = 57.89 - 19.808 \: and \: 57.89 + 19.808\n\nCI = \$38.08 \: and \:\:\$77.70\n$

Therefore, we are 95% confident that the mean repair cost for the refrigerators is within the range of ($38.08, $77.70)

14.

∠A ≅ ∠T . . . . given

AX ≅ TX . . . . given

∠AXM ≅ ∠TXH . . . . vertical angles are congruent

ΔAXM ≅ ΔTXH . . . . ASA theorem

MX ≅ HX . . . . CPCTC

___

15.

The acronyms that invoke theorems based on two or three sides being congruent are inapplicable in this case.

SSS

SAS

Quick!!! I need to do my homework
Solve: x - 1 < 3

Answers

x < 4

given x - 1 < 3 ( add 1 to both sides )

x < 4

or x ∈ ( - ∞, 4 ) ← in interval notation

Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection.Translation: (x, y)→(x−3, y)
Reflection: in the line y=−1

Answers

The image of triangle △RST after the glide reflection, which involves a translation of (x, y) → (x - 3, y) followed by a reflection in the line y = -1, is △R'S'T' with vertices R'(1, -2), S'(4, -5), and T'(3, -6).

To graph triangle △RST with vertices R(4, 1), S(7, 3), and T(6, 4), and its image after the glide reflection, we'll follow these steps:

Start by plotting the original triangle △RST using the given vertices:

R(4, 1)

S(7, 3)

T(6, 4)

Now, let's apply the translation to every vertex of the triangle.

The translation (x, y) → (x - 3, y) shifts each point 3 units to the left (in the negative x-direction).

Apply this translation to each vertex:

R' = (4 - 3, 1) = (1, 1)

S' = (7 - 3, 3) = (4, 3)

T' = (6 - 3, 4) = (3, 4)

Next, we'll apply the reflection in the line y = -1 to the translated vertices. The reflection in this line flips each point across the line.

To do this, we'll calculate the distance between each point and the line y = -1 and then move the same distance in the opposite direction.

R'' is reflected across the line y = -1 to (1, -2).

S'' is reflected across the line y = -1 to (4, -5).

T'' is reflected across the line y = -1 to (3, -6).

Now, we have the vertices of the image triangle △R'S'T'.

You can plot these points on the same graph as the original triangle to visualize the glide reflection transformation.

For similar question on image of triangle.

brainly.com/question/31515442

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Answer:

Step-by-step explanation:

Points R(4,1) S(7,3) T(6,4) after translation

R(4-3, 1) S(7-3, 3) T(6-3, 4)

R'(1, 1) S'(4, 3) T'(3, 4)

Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection

R''(1, -3) S''(4, -5) T''(3, -6)

An experiment is pulling a ball from an urn that contains 3 blue balls and 5 red balls. a.) Find the probability of getting a red ball. b.) Find the probability of getting a blue ball. c.) Find the odds for getting a red ball. d.) Find the odds for getting a blue ball.

Answers

Answer:

Step-by-step explanation:

The urn contains 3blue balls 5 red balls

a) probability of getting a red ball

P=no of favourable of outcomes /total no outcomes

P(red ball) = 5/8

b) Probability of blue ball

P(blue ball) = 3/8

c) Odds getting a red ball

odds in favour of any object = m/n

m : event to occur

n : event will not occur

Odds(red ball) = 5/3

Odds(blue) = 3/5

Solve the equation.
3* = 27
x=L(Simplify your answer.)

Answers

Answer:

3³ = 27

This is because:

3x3x3 = 27

Your answer would be 3
3x3x3
\/ x 3
9 x 3
\ /
27

1. Le Point Bookbinderypays a dividend of $1.25
per share every three
months. How many
months would it take to
earn dividends amounting
to $8.75 per share?