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love history [14]
3 years ago
12

Suppose that the number of asbestos particles in a sample of 1 squared centimeter of dust is a Poisson random variable with a me

an of 1000. What is the probability that 10 squared centimeters of dust contains more than 10110 particles?
Mathematics
1 answer:
Maslowich3 years ago
4 0

Answer:

The approximate probability that 10 squared centimeters of dust contains more than 10110 particles is 0.1357

Step-by-step explanation:

For a sample of 10 sqaured centimeters of dust, the total amount of asbestos particles has a Poisson distribution with a mean of 1000/1 * 10 = 10000.

We will approximate this probability to a normal distribution. The variance is also 10000 (because it is poisson), therefore the standard deviation is √10000 = 100. Lets call X the distribution, and W its standarization, given by

W = \frac{X-\mu}{\sigma} = \frac{X-10000}{100}

We have

P(X>10110) = P(\frac{X-10000}{100} > \frac{10110-10000}{100}) = P(W > 1,1) = 1-\phi(1,1) = 1-0.8643 = 0.1357

Where \phi is the cummulative distribution function of a standard normal distribution. The values of \phi are well known and they can be found in the attached file.

We conclude that the approximate probability that 10 squared centimeters of dust contains more than 10110 particles is 0.1357.

Download pdf
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Target is having a huge winter season sale on all of their televisions. A 42in screen tv that usually retails at $580 is marked
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Answer: You do not because the tv costs $464.

Step-by-step explanation:

First find out how much 20% of 580 is:

= 20% * 580

= $116

The television was therefore marked down by $116. The current selling price is:

= 580 - 116

= $464

<em>Since you came with $450, you will not be able to buy the television as you would be short of the $464 required. </em>

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3 years ago
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3 years ago
Sheryl's boss at always 21 pays a 5% commission on all sales. If Sheryl sells $140 worth of clothes, how much commission does sh
mariarad [96]

Answer:

She earns $7.

Step-by-step explanation:

5 percent of 140 is 7. You can think of this as taking ten percent of 140.0 by moving the decimal point one place to the left, 14, and then since 10 divided by 2 is 5, divide that by 2 and you get 7.

4 0
3 years ago
Iva wanted to train for a race by raning 10km over 3 days during the week. the first day she ran 1.37 km more than she ran on th
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Step-by-step explanation:

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