Suppose the number of messages that an inbox receives may be modeled by a Poisson distribution. If the average number of messages per hour is 18, then what is the probability it will receive between 15 and 20 messages during any given hour?

0.36427

Step-by-step explanation:

Mean = λ = 18 messages per hour

P(X = x) = (e^-λ)(λ⁻ˣ)/x!

P(X ≤ x) = Σ (e^-λ)(λ⁻ˣ)/x! (Summation From 0 to x)

But the probability required is that the messages thay come in an hour is between 15 and 20, that is, P(15 < X < 20)

P(15 < X < 20) = P(X < 20) - P(X ≤ 15)

These probabilities will be evaluated using a cumulative frequency calculator.

P(X < 20) = 0.65092

P(X ≤ 15) = poissoncdf(18, 15) = 0.28665

P(15 < X < 20) = P(X < 20) - P(X ≤ 15) = 0.65092 - 0.28665 = 0.36427.

You can use the Poisson distribution calculator here

https://stattrek.com/online-calculator/poisson.aspx

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

sorry man i accidentally pressed yes my bad

step-by-step explanation: