1) Convert the following to decimals: a) 25% b) 60% c) 72.1% d) 7% e) 9.5% f).66%

Mathematics

1 answer:

KIM [24]3 years ago

5 0

25% = 25% : 100% = 0,25 ← the end

60% = 60% : 100% = 0,6 ← the end

72,1% = 72,1% : 100% = 0,721 ← the end

7% = 7% : 100% = 0,07 ← the end

9,5% = 9,5% : 100% = 0,095 ← the end

66% = 66% : 100% = 0,66

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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

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

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

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.