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Radda [10]
3 years ago
10

In a certain community, 30% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known t

hat 27% of all the families own a cat.
What is the probability that a randomly selected family owns both a dog and a cat?
What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?
Mathematics
1 answer:
Nesterboy [21]3 years ago
3 0

Answer:

a) 0.06

b) 0.778

Step-by-step explanation:

Let's suppose a community of 100 families just to facilitate the calculation.

30% of the families own a dog

Dog = 30% of 100 = 30

20% of the families that own a dog also own a cat = 20% of 30 = 6

27% of all the families own a cat = 27% of 100 = 27

So, 6 families own a dog and a cat.

As 30 families own a dog, [30 - 6 =] 24 families own only dogs

As 27 families own a cat, [27 - 6 = ] 21 families own only cats

See picture attached.

a) What is the probability that a randomly selected family owns both a dog and a cat?

P(dog and cat) = dog ∩ cat/total = 6/100 = 0.06

b) What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?

So, only cat/total cat

P (not dog|cat) = 21/27 = 0.778

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Assume that all conditions are met. The mean of the differences was 1. 33 and the standard deviation of those differences was 2.
Maurinko [17]

The test statistic for this procedure is using two sample T-test is 0.458.

Definition of Two Sample T-test

A variation of the Student's t-test used to determine if two sample means are substantially different is known as the two sample T-test (also known as Welch's t-test, Welch's adjusted T, or unequal variances t-test). The test's degrees of freedom have been changed, which generally boosts the test's power for samples with unequal variance.

T-Test Statistic for The Procedure

It is given that mean of the differences = 1.33

And, the standard deviation of the differences, standard error = 2.90

The test static formula is given as,

t = (estimate - hypothized value) / standard error

Here,  t is the t- test statistic, and estimate is the mean of the differences.

Since it is given that all conditions are met, the hypothized value can be taken as 0

Substituting substituting estimate = 1.33 and standard error = 2.90 in the t-test statistic formula, we get,

t = (1.33-0)/2.90

or t = 0.458

learn more about t-test here:

brainly.com/question/14128303

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8 0
2 years ago
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Answer:

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Step-by-step explanation:

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    = (-2+1)/(-4+8)

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Answer:

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Step-by-step explanation:

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h is the height of the face

Substituting,

A=L^2+2Lh

For the model in this problem,

L = 12

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