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3 years ago

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Mathematics

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MArishka [77]3 years ago

7 0

Answer: i dont understand

Step-by-step explanation:

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Suppose that X has a Poisson distribution with a mean of 64. Approximate the following probabilities. Round the answers to 4 dec

o-na [289]

Answer:

(a) The probability of the event (X > 84) is 0.007.

(b) The probability of the event (X < 64) is 0.483.

Step-by-step explanation:

The random variable X follows a Poisson distribution with parameter λ = 64.

The probability mass function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0, 1, 2, ...$

(a)

Compute the probability of the event (X > 84) as follows:

P (X > 84) = 1 - P (X ≤ 84)

$=1-\sum _{x=0}^{x=84}\frac{e^{-64}(64)^{x}}{x!}\\=1-[e^{-64}\sum _{x=0}^{x=84}\frac{(64)^{x}}{x!}]\\=1-[e^{-64}[\frac{(64)^{0}}{0!}+\frac{(64)^{1}}{1!}+\frac{(64)^{2}}{2!}+...+\frac{(64)^{84}}{84!}]]\\=1-0.99308\\=0.00692\\\approx0.007$

Thus, the probability of the event (X > 84) is 0.007.

(b)

Compute the probability of the event (X < 64) as follows:

P (X < 64) = P (X = 0) + P (X = 1) + P (X = 2) + ... + P (X = 63)

$=\sum _{x=0}^{x=63}\frac{e^{-64}(64)^{x}}{x!}\\=e^{-64}\sum _{x=0}^{x=63}\frac{(64)^{x}}{x!}\\=e^{-64}[\frac{(64)^{0}}{0!}+\frac{(64)^{1}}{1!}+\frac{(64)^{2}}{2!}+...+\frac{(64)^{63}}{63!}]\\=0.48338\\\approx0.483$

Thus, the probability of the event (X < 64) is 0.483.

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3 years ago

Which pair of expressions is equivalent?

FinnZ [79.3K]

B. 4(6x) and 24x.
Hope this helps!

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3 years ago

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Question is in the picture help plss

Tom [10]

The answer to your question is going to be j because you move 3x to the right side then divide all terms by negative 4 to get y alone then you get negative 3 over 4 and then you get negative 6 over 4 which can reduce to negative 3 over 2

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3 years ago

Select the correct answer. A triangle with vertices at A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertice

erma4kov [3.2K]

Answer:

* The scale factor of the dilation is 2.5

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.

- It can become larger or smaller, but the shape of the

figure does not change.

- The scale factor, measures how much larger or smaller

the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

* In the problem

- The vertices of the triangle is A (0 , 0) , B (0 , 4) , C (6 , 0)

and its image A' is (0 , 0) , (0 , 10) , (15 , 0)

∵ 10 ÷ 4 = 2.5

∵ 15 ÷ 6 = 2.5

∴ The scale factor is 2.5

∵ 2.5 > 1

∴ The image of the triangle will be larger

* The scale factor is 2.5

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3 years ago

A math test has 12 multiplication problems and 24 division problems.

Sergio039 [100]

12/36 = 1/3

.........................................................................

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3 years ago

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