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Len [333]
3 years ago
7

Poisson Distribution LEARNING OBJECTIVE: Calculate the probability of a poisson distribution. 3.00 The average number of bridge

construction projects that take place at any one time in a certain state is 7. PIX=k) - 1e - k is the given number of event occurrences A is the average rate of event occurrences Using the Poisson distribution formula, what is the probability of exactly 4 bridge construction projects taking place at one time in this state? Answer choices are rounded to the hundredths place.
a) 0.09
b) 0.19
c) 0.06
d) 0.05
Mathematics
1 answer:
ira [324]3 years ago
5 0

Answer:

the required probability is 0.09

Option  a) 0.09 is the correct Answer.

Step-by-step explanation:

Given that;

mean μ  = 7  

x = 4

the probability of exactly 4 bridge construction projects taking place at one time in this state = ?

Using the Poisson probability formula;

P( X=x ) = ( e^-μ × u^x) / x!

we substitute

P(X = 4) = (e⁻⁷ × 7⁴) / 4!

= 2.1894 / 24

= 0.0875 ≈ 0.09

Therefore the required probability is 0.09

Option  a) 0.09 is the correct Answer.

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Given:

The figure of a rhombus QRST.

To find:

A. The value of x.

B. The measure of angle RQP.

Solution:

A. We need to find the value of x.

We know that the diagonals of a rhombus are perpendicular bisectors. It means the angles on the intersection of diagonals are right angles.

m\angle RPS=90^\circ                       [Right angle]

(5x+15)^\circ=90^\circ

(5x+15)=90

5x=90-15

5x=75

Divide both sides by 5.

x=\dfrac{75}{5}

x=15

Therefore, the value of x is 15.

B. We need to find the measure of angle RQP.

From the given figure, it is clear that

m\angle RQP=(2x+3)^\circ

Putting x=15, we get

m\angle RQP=(2(15)+3)^\circ

m\angle RQP=(30+3)^\circ

m\angle RQP=33^\circ

Therefore, the measure of angle RQP is 33 degrees.

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3 years ago
Write and solve the sentence as an inequality.<br> A number minus 3 is less than -5.
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Answer:

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Step-by-step explanation:

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A person purchased a slot machine and tested it by playing it 1,137 times. There are 10 different categories of outcomes, includ
ivann1987 [24]

Answer:

p_v= P(\chi^2_{9}>11.517)=0.2419

And on this case if we see the significance level given \alpha=0.1 we see that p_v>alpha so we fail to reject the null hypothesis that the observed outcomes agree with the expected frequencies at 10% of significance.

Step-by-step explanation:

A chi-square goodness of fit test determines if a sample data obtained fit to a specified population.

p_v represent the p value for the test

O= obserbed values

E= expected values

The system of hypothesis for this case are:

Null hypothesis: O_i = E_i[/tex[Alternative hypothesis: [tex]O_i \neq E_i

The statistic to check the hypothesis is given by:

\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}

On this case after calculate the statistic they got: \chi^2 = 11.517

And in order to calculate the p value we need to find first the degrees of freedom given by:

df=n-1=10-1=9, where k represent the number of levels (on this cas we have 10 categories)

And in order to calculate the p value we need to calculate the following probability:

p_v= P(\chi^2_{9}>11.517)=0.2419

And on this case if we see the significance level given \alpha=0.1 we see that p_v>alpha so we fail to reject the null hypothesis that the observed outcomes agree with the expected frequencies at 10% of significance.

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