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calculate the variance and standard deviation for the following samples set of data. 83.6,92.3,56.5,43.8,77.1,66.7. (Do not round intermediate calculation. Round your final answers and the nearest tenth.)

Answers

Answer 1

Answer:

Answer:

Variance: 322.4479999999996

Standard Deviation: 17.956837137981722

Answer 2

Answer:

Final answer:

To calculate the variance and standard deviation for the given sample set of data, find the sample mean, calculate the squared differences, and then find the sample variance and standard deviation.

Explanation:

To calculate the variance and standard deviation for the given sample set of data (83.6, 92.3, 56.5, 43.8, 77.1, 66.7), follow these steps:

Calculate the sample mean by adding all the values together and dividing by the total number of values: (83.6 + 92.3 + 56.5 + 43.8 + 77.1 + 66.7) / 6 = 69.8.
Calculate the squared differences between each value and the sample mean: (83.6 - 69.8)^2, (92.3 - 69.8)^2, (56.5 - 69.8)^2, (43.8 - 69.8)^2, (77.1 - 69.8)^2, (66.7 - 69.8)^2.
Calculate the sample variance by summing up the squared differences and dividing by (n-1), where n is the total number of values: (83.6 - 69.8)^2 + (92.3 - 69.8)^2 + (56.5 - 69.8)^2 + (43.8 - 69.8)^2 + (77.1 - 69.8)^2 + (66.7 - 69.8)^2 = 300.46. Sample variance = 300.46 / 5 = 60.1.
Calculate the sample standard deviation by taking the square root of the sample variance: √60.1 = 7.79. Rounded to the nearest tenth, the sample standard deviation = 7.8.

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Is 4:3 and 3:4 equivalent

Answers

Answer: No

Step-by-step explanation:

sorry but nope...........

Diego makes green paint by mixing 10 tablespoons of yellow paint and 2 tablespoons of blue paint. Which of these mixtures produce the same shade of green paint as Diego’s mixture?Select all that apply.

Group of answer choices

For every 5 tablespoons of blue paint, mix in 1 tablespoon of yellow paint.

Mix tablespoons of blue paint and yellow paint in the ratio 1:5.

Mix 11 tablespoons of yellow paint and 3 tablespoons of blue paint.

Mix tablespoons of yellow paint and blue paint in the ratio 15 to 3.

Answers

The correct answer choices are For every 5 tablespoons of blue paint, mix in 1 tablespoon of yellow paint, Mix tablespoons of blue paint and yellow paint in the ratio 1:5 and Mix tablespoons of yellow paint and blue paint in the ratio 15 to 3.

What is ratio ?

Ratio represents how much one quantity is present relative to the other quantity and written in simplest form.

According to the given question Diego makes green paint by mixing 10 tablespoons of yellow paint and 2 tablespoons of blue paint.

∴ For every 5 tablespoon of blue paint we have to mix 1 table spoon of yellow paint.

5 table spoon of blue paint = 1 table spoon of yellow paint.

This can also be written in ratio form as blue paint:yellow paint = 1:5.

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Answer: Mix 11 tablespoons of yellow paint and 3 tablespoons of blue paint.

Interest centers around the life of an electronic component. Let A be the event that the component fails a particular test and B be the event that the component displays strain but does not actually fail. Event A occurs with probability 0.39, and event B occurs with probability 0.24. A) What is the probability that the component does not fail the test?
B) What is the probability that a component works perfectly well (i.e., neither displays strain nor fails the test)?
C) What is the probability that the component either fails or shows strain in the test?

Answers

Answer: a. 0.61

b. 0.37

c. 0.63

Step-by-step explanation:

From the question,

P(A) = 0.39 and P(B) = 0.24

P(success) + P( failure) = 1

A) What is the probability that the component does not fail the test?

Since A is the event that the component fails a particular test, the probability that the component does not fail the test will be P(success). This will be:

= 1 - P(A)

= 1 - 0.39

= 0.61

B) What is the probability that a component works perfectly well (i.e., neither displays strain nor fails the test)?

This will be the probability that the component does not fail the test minus the event that the component displays strain but does not actually fail. This will be:

= [1 - P(A)] - P(B)

= 0.61 - 0.24

= 0.37

C) What is the probability that the component either fails or shows strain in the test?

This will simply be:

= 1 - P(probability that a component works perfectly well)

= 1 - 0.37

= 0.63

The tread life on tires produced at one factory has a standard deviation of sigma equals 4 comma 000 miles. What is the standard deviation of the sampling distribution of the sample means given the sample size is 4

Answers

Answer:

$\sigma_x = 2000$

Step-by-step explanation:

Given

$\sigma = 4000$

$n = 4$

Required

The sample standard deviation

The sample standard deviation cannot be calculated directly. However, we can use the value of standard error because standard error approximates to sample standard deviation.

So, we have:

$\sigma_x = (\sigma)/(\sqrt n)$