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Mashutka [201]
3 years ago
14

Graph: y-3 = 1/2 (x+2)

Mathematics
1 answer:
Luda [366]3 years ago
4 0

Answer:

Step-by-step explanation:

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The concentration of particles in a suspension is 50 per mL. A 5 mL volume of the suspension is withdrawn. a. What is the probab
kolezko [41]

Answer:

(a) 0.6579

(b) 0.2961

(c) 0.3108

(d) 240

Step-by-step explanation:

The random variable <em>X</em> can be defined as the number of particles in a suspension.

The concentration of particles in a suspension is 50 per ml.

Then in 5 mL volume of the suspension the number of particles will be,

5 × 50 = 250.

The random variable <em>X</em> thus follows a Poisson distribution with parameter, <em>λ</em> = 250.

The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.  

The mean of the approximated distribution of X is:

μ = λ  = 250

The standard deviation of the approximated distribution of X is:

σ = √λ  = √250 = 15.8114

Thus, X\sim N(250, 250)

(a)

Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:

P(235

                             =P(-0.95

Thus, the value of P (235 < <em>X</em> < 265) = 0.6579.

(b)

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

P(48

                             =P(-0.28

Thus, the value of P(48.

(c)

A 10 mL sample is withdrawn.

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

P(48

                             =P(-0.40

Thus, the value of P(48.

(d)

Let the sample size be <em>n</em>.

P(48

                             0.95=P(-z

The value of <em>z</em> for this probability is,

<em>z</em> = 1.96

Compute the value of <em>n</em> as follows:

z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}\\\\1.96=\frac{48-50}{15.8114/\sqrt{n}}\\\\n=[\frac{1.96\times 15.8114}{48-50}]^{2}\\\\n=240.1004\\\\n\approx 241

Thus, the sample selected must be of size 240.

5 0
3 years ago
G(-2, 5), H(6, 5), J(6, -1) 17 Find the coordinates of the centroid.
eimsori [14]
Hjjkbcyjkkhjiihbkoougnig
4 0
3 years ago
One book has 394 pages. Another book has 102 pages more than the first. How many pages are in both books?
Sedbober [7]

Answer:

B

Step-by-step explanation:

Because i said so

6 0
3 years ago
Read 2 more answers
What factors does Jenna need to model for the sides?
gladu [14]
I don’t see a picture or anything? Can you explain more I don’t know the sides
4 0
3 years ago
A group of adults and students went on a class trip to Washington, DC. The number of male students was 1 more than 7 times the n
sp2606 [1]
Let the number of adults be x, then number of male students is 1 + 7x and the number of female students is (1 + 7x)/2.
x + 1 + 7x + (1 + 7x)/2 = 82
2x + 2 + 14x + 1 + 7x = 164
23x = 164 - 2 - 1 = 161
x = 161/23 = 7

Therefore, number of male students is 1 + 7(7) = 1 + 49 = 50
and the number of female students is 50/2 = 25.
5 0
3 years ago
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