Mathematics, 22.12.2021 06:50 christopher766

According to the Ministry of Public Education, schools in Samarkand have closed an average of 24 days each year due to some type of emergencies. Assume that the number of school closure days can be approximated by a Poisson distribution. What is the probability that a randomly chosen school in Samarkand will close for 1 or 2 days next month?

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Using the Poisson distribution, it is found that there is a 0.5414 = 54.14% probability that a randomly chosen school in Samarkand will close for 1 or 2 days next month.

We have the mean in an interval, hence, the Poisson distribution is used.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

The parameters are:

x is the number of successes e = 2.71828 is the Euler number $\mu$ is the mean in the given interval.

Average of 24 days each year, considering that a year has 12 months, the monthly mean is of $\mu = \frac{24}{12} = 2$

Then:

$P(1 \leq X \leq 2) = P(X = 1) + P(X = 2)$

In which

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

$P(X = 1) = \frac{e^{-2}2^{1}}{(1)!} = 0.2707$

$P(X = 2) = \frac{e^{-2}2^{2}}{(2)!} = 0.2707$

$P(1 \leq X \leq 2) = P(X = 1) + P(X = 2) = 0.2707 + 0.2707 = 0.5414$

0.5414 = 54.14% probability that a randomly chosen school in Samarkand will close for 1 or 2 days next month.

To learn more about the Poisson distribution, you can take a look at

Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

Answer from: Quest

the equation is not included but the answer is (1.50, 2.00, 2.75)

step-by-step explanation:

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