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elena-s [515]
2 years ago
9

Within a computer program, the number of bugs (i.e., coding errors) per lines of code has a Poisson distribution with an average

of fifteen bugs per 1,000 lines. a. Find the probability that there will be exactly eight bugs in 1,000 lines of code. b. Find the probability that there will be at least eight bugs in 1,000 lines of code. c. Find the probability that there will be at least one bug in 1,000 lines of code. d. Find the probability that there will be no more than
Mathematics
1 answer:
Alex Ar [27]2 years ago
8 0

Answer:

P(X=8) = 0.0194

P(X \ge 8)= 0.9820

P(X \ge 1)= 1

P(X\le 1) = 0.0000049

Step-by-step explanation:

Given

\lambda = 15

Poisson distribution is given by:

P(X=x) = \frac{\lambda^x e^{-\lambda}}{x!}

Solving (a): 8 bugs

This implies that:

x = 8

So, we have:

P(X=8) = \frac{15^8 * e^{-15}}{8!}

P(X=8) = \frac{783.99418938}{40320}

P(X=8) = 0.0194

Solving (b): At least 8 bugs

This is represented as: P(X \ge 8)

Using complement rule:

P(X \ge 8)= 1 - P(X

Where

P(X

P(X

P(X

P(X

P(X

P(X

So:

P(X \ge 8)= 1 - P(X

P(X \ge 8)= 1 - 0.0180

P(X \ge 8)= 0.9820

Solving (c): At least 1

This is represented as: P(X \ge 1)

Using complement rule:

P(X \ge 1)= 1 - P(X

P(X

P(X

P(X

P(X

So:

P(X \ge 1)= 1 - P(X

P(X \ge 1)= 1 - e^{-15

P(X \ge 1)= 0.99999969409

P(X \ge 1)= 1

Solving (d): Not more than 1

This implies at most 1.

It is represented as:

P(X\le 1)

It is calculated using:

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

P(X = 0) = e^{-15}

P(X=1) = \frac{15^1 * e^{-15}}{1!}

P(X=1) = 15 * e^{-15}

So:

P(X\le 1) = e^{-15} + 15 * e^{-15}

P(X\le 1) = 0.00000489443

P(X\le 1) = 0.0000049

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Sav [38]

Answer:

Three rectangular boxes having bases 4 cubic feet, 3 cubic feet and 2 cubic feet respectively will be required to hold 16 cubic feet of soil.

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Step-by-step explanation:

The total soil to be held is 16 cubic feet.

The volume of a rectangular box is given by the product, lbh, where l is the length, b is the base and h is the height.

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Since, all the three boxes have to be rectangular in shape, the base has to be more than the other two dimensions to get the required volumes as explained above.

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The equation in spherical coordinates will be a constant, as we are describing a spherical shell.

r(φ, θ) = 8 units.

<h3>How to rewrite the equation in spherical coordinates?</h3>

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Then the equation:

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