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topjm [15]
2 years ago
8

A building is examined by policemen with four dogs that are trained to detect the scent of explosives. if there are explosives i

n a certain building, and each dog detects them with probability 0.6, independently of other dogs, what is the probability that the explosives will be detected by at least one dog?
Mathematics
1 answer:
Elza [17]2 years ago
4 0
The probability of a dog finding the explosive is .6
The probability of a dog will not find the explosive is .4
The probability that no dogs will find the explosive is .4^4
The probability that at least 1 dog will find the explosive is 1 - .4^4.
this equals 1 - .0256 which equals .9744
the probability that at least 1 dog will find the explosive is .9744.
if you wanted to find the probability that exactly x out of 4 will find the explosives, then you would use the following formula:
p(0) = 4c0 * .6^0 * .4^4
p(1) = 4c1 * .6^1 * .4^3
p(2) = 4c2 * .6^2 * .4^2
p(3) = 4c3 * .6^3 * .4^1
p(4) = 4c4 * .6^4 * .4^0

 4c0 and 4c4 = 1 each
4c1 and 4c3 = 4 each
4c2 = 6
probabilities become:
p(0) = .0256
p(1) = .1536
p(2) = .3456
p(3) = .3456
p(4) = .1296
sum of the probabilities equals 1 as it should.
combination formula of ncx = n! / ((n-x)!x!)
if you add up the probabilities for 1 and 2 and 3 and 4 dogs finding the explosives, you will see that it is equal to 1 - probability that no dogs find the explosives.
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Answer:

The confidence Interval = (0.329, 0.391)

Step-by-step explanation:

Formula for the Confidence Interval for proportion =

p ± z × √p(1 - p)/n

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From the question

n = 900 people

x = 36% of 900 people

= 36/100 × 900

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z = z score of 95% confidence Interval

z = 1.98

p = x/n

= 324/900

= 0.36

Confidence Interval = p ± z × √p(1 - p)/n

= 0.36 ± 1.96 × √0.36 (1 - 0.36)/900

= 0.36 ± 1.96 ×√0.36 (0.64)/900

= 0.36 ± 1.96 × √0.000256

= 0.36 ± 1.96 × 0.016

= 0.36 ± 0.03136

Confidence Interval = 0.36 ± 0.03136

= 0.36 - 0.03136

= 0.32864

Approximately to 3 decimal places = 0.329

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= 0.39136

Approximately to 3 decimal places = 0.391

Therefore, the 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws = (0.329, 0.391)

7 0
3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

Substitution property of equality

Step-by-step explanation:

Given

4x + 9 = 15 and x = 2y + 1

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Required

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This is so because:

Substitution property of equality states that

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So if x = 2y + 1, then 2y + 1 can be substituted for x in 4x + 9 = 15

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4x + 9 = 15  becomes

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