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gtnhenbr [62]
3 years ago
13

Can someone please help me with a probability question??

Mathematics
1 answer:
yawa3891 [41]3 years ago
4 0
Sure, what's the question?
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8000 liters

Step-by-step explanation:

There are 1000 liters in a kiloliter, so you would multiply both sides by 8.

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What's 5 to the fourth power over 5
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3 years ago
I need help on figuring out the two ways.
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4 0
3 years ago
Two cars depart an intersection.
patriot [66]

Answer:

The distance between them after 1 hour and 30 minutes will be of 63.64 miles.

Step-by-step explanation:

This question can be solved using the Pythagorean Theorem.

Both cars travel at a constant speed of 30 miles per hour. So, after 1 hour and 30 minutes, which is 1 and a half hour, they will have traveled 30*1.5 = 45 miles.

The distance between them is the hypotenuse of a right triangle, in which the sides are 45. So

d^2 = 45^2 + 45^2

d = \sqrt{45^2 + 45^2}

d = 63.64

The distance between them after 1 hour and 30 minutes will be of 63.64 miles.

4 0
3 years ago
In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.3 quakes per year. Let X be the number of quakes in a given
hichkok12 [17]

Answer:

a) Earthquakes are random and independent events.

b) There is an 85.71% probability of fewer than three quakes.

c) There is a 0.51% probability of more than five quakes.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

In this problem, we have that:

In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.3 quakes per year, so \mu = 1.3

(a) Justify the use of the Poisson model.

Earthquakes are random and independent events.

You can't predict when a earthquake is going to happen, or how many are going to have in a year. It is an estimative.

(b) What is the probability of fewer than three quakes?

This is P(X < 3)

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

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

P(X = 0) = \frac{e^{-1.3}*1.3^{0}}{(0)!} = 0.2725

P(X = 1) = \frac{e^{-1.3}*1.3^{1}}{(1)!} = 0.3543

P(X = 2) = \frac{e^{-1.3}*1.3^{2}}{(2)!} = 0.2303

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2725 + 0.3543 + 0.2303 = 0.8571

There is an 85.71% probability of fewer than three quakes.

(c) What is the probability of more than five quakes?

This is P(X > 5)

We know that either there are 5 or less earthquakes, or there are more than 5 earthquakes. The sum of the probabilities of these events is decimal 1.

So

P(X \leq 5) + P(X > 5) = 1

P(X > 5) = 1 - P(X \leq 5)

In which

P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

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

P(X = 0) = \frac{e^{-1.3}*1.3^{0}}{(0)!} = 0.2725

P(X = 1) = \frac{e^{-1.3}*1.3^{1}}{(1)!} = 0.3543

P(X = 2) = \frac{e^{-1.3}*1.3^{2}}{(2)!} = 0.2303

P(X = 3) = \frac{e^{-1.3}*1.3^{3}}{(3)!} = 0.0980

P(X = 4) = \frac{e^{-1.3}*1.3^{4}}{(4)!} = 0.0324

P(X = 5) = \frac{e^{-1.3}*1.3^{5}}{(5)!} = 0.0084

P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.2725 + 0.3543 + 0.2303 + 0.0980 + 0.0324 + 0.0084 = 0.9949

Finally

P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9949 = 0.0051

There is a 0.51% probability of more than five quakes.

5 0
3 years ago
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