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attashe74 [19]
3 years ago
15

I write out all the whole numbers, starting from 1. If I wrote 1994 digits altogether, what was the last complete number I wrote

down?
Mathematics
1 answer:
Nataly_w [17]3 years ago
3 0

Answer:

You wrote the numbers from 1 to 9: 9 digits.

You wrote the numbers from 10 to 99: 90*2 = 180 digits.

You have written 189 digits.

Then you wrote another 1994 - 189 = 1805

All the numbers from 100 to 999 have 3 digits

So you wrote 1805/3 = 601 2/3

This means 601 full numbers and 2 digits from the 602. number.

So 100 + 601 - 1 = 700 was the last number you wrote.

Do you agree?


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Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

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The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

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At most 3 intervals?

This is P = f(0) + f(1) + f(2) + f(3)

f(x) = (1-p)^{x}p

f(0) = (1-0.383)^{0}*(0.383) = 0.383

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f(2) = (1-0.383)^{2}*(0.383) = 0.146

Previously in this exercise, we found that f(3) = 0.09

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P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855

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(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4).

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