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musickatia [10]
2 years ago
13

Q1 ).The number of white corpuscles on a slide has a Poisson distribution with mean 4.5.

Mathematics
1 answer:
dybincka [34]2 years ago
7 0

The most likely number of white corpuscles om a slide is 4 ,the probability of obtaining this number 4 is 0.190 , probability of obtaining at least two white corpuscles in total on the two slides is 0.999.

Attending to the first question

<h3>What is Poison Distribution ?</h3>

Poisson Distribution is used for an independent event to find its  probability in a fixed interval of time .

Let X be the number of white corpuscles on a slide, then X~Pois(4.5)

a) We have to find the most likely number of white corpuscles on  a slide , which means expected value of Poise(4.5)

The expected value of Poisson distribution with mean λ is equal to λ.

Therefore the expected value is 4.5.

 the number of corpuscles cannot be non-integer,

To find the most likely number in one experiment,

determine it between 4 and 5.

In the common case P(X=k) when X~Poise(λ) is equal to \frac {\lambda^{k}} {k!}}e^{-\lambda}

,\rm e^{-\lambda}  is a constant in terms of k

​so the point is to find out what is greater  :   {\frac {4.5^4} {4!}} or {\frac {4.5^5} {5!}}

 {\frac {4.5^5} {5!}}={\frac {4.5^4} {4!}} * {\frac {4.5} 5}

{\frac {4.5} 5} < 1

So, {\frac {4.5^4} {4!}} is greater

So, the most likely number of white corpuscles om a slide is 4.

b)  the probability of obtaining this number 4 is

P(X = 4)

= {\frac {4.5^4} {4!}}e^{-4.5}=0.190

c) Let Y be the total number of corpuscles on two screens.

Y=X{\scriptscriptstyle 1}+X{\scriptscriptstyle 2}Y=X1+X2 ,

where X{\scriptscriptstyle 1}, X{\scriptscriptstyle 2}  - number of corpuscles on the first and second slide respectively.

Then Y = Poise(4.5 + 4.5) = Poise(9)

the probability, correct to three decimals places of obtaining at least two white corpuscles in total on the two slides

The goal is to find P(Y ≥ 2)

Therefore the probability less than 2 will be subtracted from the total probability i.e. 1

P(Y ≥ 2 ) = 1 - P (Y=0) - P(Y=1)

= 1-{\frac {9^0} {0!}}e^{-9}-{\frac {9^1} {1!}}e^{-9}=1-10e^{-9}=0.999

To know more about Poisson Distribution

brainly.com/question/17280826

#SPJ1

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Vinvika [58]

Answer:

(a) 0.0256

(b) 0.2944

Step-by-step explanation:

For solving this exercise we can apply the binomial distribution. The equation that give as the probability is:

P(x,n,p)=(nCx)*p^{x} *(1-p)^{n-x}

Where n is the number of identical events, p is the probability that the event has a success and x is the number of success in the n identical events.

Additionally, nCx is calculated as:

nCx=\frac{n!}{x!(n-x)!}

So, in this case we have 2 identical events because we are going to select two people randomly and the probability p of success is the probability that the person is allergic to pollen and this probability is 16%.

Then, for the first case, x is 2 because their are asking for the probability that both are allergic to pollen. Replacing the values of x, n and p we get:

P(2,2,0.16)=(2C2)*0.16^{2} *(1-0.16)^{2-2}

P(2,2,0.16)=0.0256

For the second case, their are asking for the probability that at least one is allergic to pollen, that means that we need to sum the probability that both are allergic to pollen with the probability that just one is allergic to pollen.

Using the same equation to calculate P(1,2,0.16) we get:

P(1,2,0.16)=(2C1)*0.16^{1} *(1-0.16)^{2-1}

P(1,2,0.16)=0.2688

So, the probability that at least one person is allergic to pollen is 0.2944 and it is calculated as:

0.0256 + 0.2688 = 0.2944

7 0
3 years ago
In a sample of 57 temperature readings taken from the freezer of a restaurant, the mean is 29.6 degrees and the population stand
Natalka [10]

Answer:

(29.14 ; 30.06)

Step-by-step explanation:

Given that'

Sample size (n) = 57

Mean (m) = 29.6

Population standard deviation (σ) = 2.7

Confidence interval = 80%

= (1 - 0.8) / 2 = 0.1

Mean ± z * σ/√n

Using the Z probability calculator : Z0. 1 = 1.28

Hence,

29.6 ± 1.28 * (2.7 / √57)

29.6 - (1.28 * 0.3576237) ; 29.6 + (1.28 * 0.3576237)

29.142241664 ; 30.057758336

(29.14 ; 30.06)

8 0
3 years ago
Find the perimeter of the triangle with vertices ​A(negative 2​,2​,3​), ​B(4​,negative 4​,3​), and ​C(7​,6​,4​).
gayaneshka [121]

Answer:

P\approx 28.872\,\text{units}

Step-by-step explanation:

We are given coordinates of each of the vertices of the triangle ABC, hence we can use the distance formula to find the lengths of each of the side.

the distance formula is generally written as:

r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}

for the side AB: A(-2,2,3) and B(4,-4,3)

AB = \sqrt{(-2-4)^2+(2-(-4))^2+(3-3)^2}

AB = \sqrt{(-6)^2+(6)^2+(3-3)^2}

AB = \sqrt{72}

for the side BC: B(4,-4,3) and C(7,6,4)

BC = \sqrt{(4-7)^2+((-4)-6)^2+(3-4)^2}

BC = \sqrt{110}

for the side CA: C(7,6,4) and A(-2,2,3)

CA = \sqrt{(7-(-2))^2+(6-2)^2+(4-3)^2}

CA = \sqrt{98}

Now we all the sidelengths:

to find the perimeter we need to just sum the three side lengths:

P = AB + BC + CA

P = \sqrt{72} + \sqrt{110} + \sqrt{98}

P\approx 28.872\,\text{units}

this is the perimeter of triangle ABC

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8x plus 8y equals 8. 8x plus 2y equals 28. Find x and y
alukav5142 [94]

Answer:

x,y = 13/3, -10/3

Step-by-step explanation:

8x+8y=8

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6 0
2 years ago
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