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Otrada [13]
3 years ago
15

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.8 per year. a. Find t

he probability​ that, in a​ year, there will be 3 hurricanes. b. In a 45​-year ​period, how many years are expected to have 3 ​hurricanes? c. How does the result from part​ (b) compare to a recent period of 45 years in which 4 years had 3 ​hurricanes? Does the Poisson distribution work well​ here?
Mathematics
1 answer:
maw [93]3 years ago
8 0

Answer:

a. 0.098

b. 4.41

c. Yes, it does.

Step-by-step explanation:

a.

The Poisson distribution's equation is:

P(x) = (nˣ*e⁻ⁿ)/x!

where P is the probability, n is mean number, and x the number of the event happens, so:

P(3) = \frac{5.8^3*e^{-5.8}}{3!}

P(3) = 0.098

b.

For 45 years, the years that are expected to have 3 hurricanes are

P(3) * 45 = 0.098*45 = 4.41

c.

Yes, it does. The Poisson distribution works well because the observed value of the number of years that 3 hurricanes occur is 45-year period is very close to the calculated value.

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triple one number added to another number is 22. if the second number is equal to 8 less than 2 times the first number, find the
Scrat [10]

Answer:

  • 6 and 4

Step-by-step explanation:

Let the numbers are x and y.

<u>Given:</u>

  • 3x + y = 22
  • y = 2x - 8

<u>Solve by substitution:</u>

  • 3x + 2x - 8 = 22
  • 5x = 22 + 8
  • 5x = 30
  • x = 6

<u>Find y:</u>

  • y = 2*6 - 8 = 12 - 8 = 4
4 0
2 years ago
Cost To Store : $110 Markup : 140%
eimsori [14]
If you are talking about $110 being increased by 140% then the answer is $264
5 0
2 years ago
For about $1 billion in new space shuttle expenditures, NASA has proposed to install new heat pumps, power heads, heat exchanger
11111nata11111 [884]

Answer:

The probability of one or more catastrophes in:

(1) Two mission is 0.0166.

(2) Five mission is 0.0410.

(3) Ten mission is 0.0803.

(4) Fifty mission is 0.3419.

Step-by-step explanation:

Let <em>X</em> = number of catastrophes in the missions.

The probability of a catastrophe in a mission is, P (X) = p=\frac{1}{120}.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.

The probability mass function of <em>X </em>is:

P(X=x)={n\choose x}\frac{1}{120}^{x}(1-\frac{1}{120})^{n-x};\x=0,1,2,3...

In this case we need to compute the probability of 1 or more than 1 catastrophes in <em>n</em> missions.

Then the value of P (X ≥ 1) is:

P (X ≥ 1) = 1 - P (X < 1)

             = 1 - P (X = 0)

             =1-{n\choose 0}\frac{1}{120}^{0}(1-\frac{1}{120})^{n-0}\\=1-(1\times1\times(1-\frac{1}{120})^{n-0})\\=1-(1-\frac{1}{120})^{n-0}

(1)

Compute the compute the probability of 1 or more than 1 catastrophes in 2 missions as follows:

P(X\geq 1)=1-(1-\frac{1}{120})^{2-0}=1-0.9834=0.0166

(2)

Compute the compute the probability of 1 or more than 1 catastrophes in 5 missions as follows:

P(X\geq 1)=1-(1-\frac{1}{120})^{5-0}=1-0.9590=0.0410

(3)

Compute the compute the probability of 1 or more than 1 catastrophes in 10 missions as follows:

P(X\geq 1)=1-(1-\frac{1}{120})^{10-0}=1-0.9197=0.0803

(4)

Compute the compute the probability of 1 or more than 1 catastrophes in 50 missions as follows:

P(X\geq 1)=1-(1-\frac{1}{120})^{50-0}=1-0.6581=0.3419

6 0
3 years ago
Please help and explain <br>Which represents the value of x?​
IRINA_888 [86]
The first option would be the correct answer because you have the outer angle at 121 degrees and a straight angle adds up to 180 degrees so 121 - 180 = 59. Now you have the original angle on the inside which is 47 degrees and you add 47 + 59 and you get 106. Since this shape is a triangle you would do 180 - 106 to get your last angle which would be 74. Hope this helps!
6 0
2 years ago
a baseball and a bat cost $1.10 and if this bat costs .10 cents more than the ball. how much did the ball cost?
kari74 [83]
<u>Define x:</u>
Let the cost of the ball be x.
Ball = x
Bat = x + 0.1

<u>The total cost is $1.10:</u>
x + x + 0.1 = 1.1
2x + 0.1 = 1.1
2x = 1
x = 0.5

<u>Find the cost of the bat and the ball:</u>
ball = x = $0.50
bat = x + 0.1 = 0.5 + 0.1 = $0.60

Answer: The ball cost $0.50


8 0
3 years ago
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