National polls are often conducted by asking the opinions of a few thousand adults nationwide and using them to infer the opinio
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The probability that, for any day, the number of special orders sent out will be exactly 3 is 0.1633.
<h3>What are some of the properties of Poisson distribution?</h3>The Poisson distribution is a discrete probability distribution that describes the likelihood of a specific number of events occurring in a specified span of time or space, if these events occur at a constant mean rate and regardless of the time since the last occurrence.
Let X ~ Pois(λ)
Then we have:
E(X) = λ = Var(X)
Since standard deviation is the square root (positive) of variance,
Thus,
The standard deviation of X =
Its probability function is given by
Given the mean is 4.2.
We have to find the probability that on any day, the number of special orders sent out will be exactly 3. Therefore, the value of x will be 5.
Using the Poisson distribution,
Hence, the probability that, for any day, the number of special orders sent out will be exactly 3 is 0.1633.
Learn more about Poisson distribution here:
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Answer:
A)
B) 89.157 million tons.
C) In year 2017.
Step-by-step explanation:
We have been given that world poultry production was 77.2 million tons in the year 2004 and increasing at a continuous rate of 1.6% per year.
A). We know that a continuous growth function is in form , where,
a = Initial value,
k = Growth rate in decimal form.
Upon substituting our given values, we will get:
Therefore, our required function would be , where, P represents world poultry production, in million tons, as a function of the number of years, t, since 2004.
B) To find the world poultry production in the year 2013, we will substitute in above formula as:
Therefore, the world poultry production in the year 2013 would be 89.157 million tons.
C) To find the number of years it will take for world poultry production to be over 95 million tons, we will equate our function with 95 as:
Divide both sides by 77.2:
Take natural log of both sides:
Divide both sides by 0.016:
Therefore, 13 years after in 2017 world poultry production goes over 95 million tons.