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Svetlanka [38]
3 years ago
11

According to national data, 5.1% of burglaries are cleared with arrests. A new detective is assigned to six different burglaries

. What is the probability that at least one of them is cleared with an arrest
Mathematics
1 answer:
blagie [28]3 years ago
8 0

Answer:

26.95% probability that at least one of them is cleared with an arrest

Step-by-step explanation:

For each burglary, there are only two possible outcomes. Either it is cleared, or it is not. The probability of a burglary being cleared is independent of other burglaries. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

5.1% of burglaries are cleared with arrests.

This means that p = 0.051

A new detective is assigned to six different burglaries.

This means that n = 6

What is the probability that at least one of them is cleared with an arrest?

Either none are cleared, or at least one is. The sum of the probabilities of these events is 100% = 1. So

P(X = 0) + P(X \geq 1) = 1

We want P(X \geq 1)

Then

P(X \geq 1) = 1 - P(X = 0)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{6,0}.(0.051)^{0}.(0.949)^{6} = 0.7305

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7305 = 0.2695

26.95% probability that at least one of them is cleared with an arrest

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Answer:

(x-10)(x+10)

Step-by-step explanation:

x^2 – 100

This is the difference of squares

x^2 - 10^2

We know that (a^2 - b^2) = (a-b) (a+b)

(x-10)(x+10)

3 0
3 years ago
The angles of elevation froma point X to the top of flagpoles A and B are 35* and 45* respectively. If X lies in the middle of t
BartSMP [9]

Let AB = t. And since X lies in the middle, so AX=BX = t/2 .

Let the height of the smaller flagpole is AO and of larger flagpole is BP .

Using tangent ratio rule in each triangle, we will get

tan 35 =\frac{AO}{t/2} , tan 45= \frac{BP}{t/2} // AO = \frac{t*tan35}{2},  BP=\frac{t*tan45}{2}

And there ratio is

\frac{AO}{BP}= \frac{tan 35}{tan 45}=\frac{0.7}{1}

5 0
3 years ago
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13. \frac{4}{10} ,  \frac{4}{100}

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8 0
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A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two
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3 years ago
Read 2 more answers
The tensile strength of a metal part is normally distributed with mean 40 pounds and standard deviation 5 pounds. If 50,000 part
nalin [4]

Answer:

a) how many would you expect to fail to meet a minimum specification limit of 35-pounds tensile strength?

7933 parts

b) How many would have a tensile strength in excess of 48 pounds?

2739.95 parts

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

a) how many would you expect to fail to meet a minimum specification limit of 35-pounds tensile strength?

z = (x-μ)/σ

x = 35 μ = 40 , σ = 5

z = 35 - 40/5

= -5/-5

= -1

Determining the Probability value from Z-Table:

P(x<35) = 0.15866

Converting to percentage = 15.866%

We are asked how many will fail to meet this specification

We have 50,000 parts

Hence,

15.866% of 50,000 parts will fail to meet the specification

= 15.866% of 50,000

= 7933 parts

Therefore, 7933 parts will fail to meet the specifications.

b) How many would have a tensile strength in excess of 48 pounds?

z = (x-μ)/σ

x = 48 μ = 40 , σ = 5

z = 48 - 40/5

z = 8/5

z = 1.6

P-value from Z-Table:

P(x<48) = 0.9452

P(x>48) = 1 - P(x<48)

1 - 0.9452

= 0.054799

Converting to percentage

= 5.4799%

Therefore, 5.4799% will have an excess of (or will be greater than) 48 pounds

We are asked, how many would have a tensile strength in excess of 48 pounds?

This would be 5.4799% of 50,000 parts

= 5.4799% × 50,000

= 2739.95

Therefore, 2739.95 parts will have a tensile strength excess of 48 pounds

4 0
3 years ago
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