Mathematics, 04.07.2020 14:01 natekotterman

Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance. Assume the variable follows a Poisson distribution. What is the probability that the company will receive more than 20 calls per hour? Round answer to 4 decimal places.

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Answer from: 4804102262

0.0409 = 4.09% probability that the company will receive more than 20 calls per hour

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the normal distribution.

Poisson distribution:

random variable is given by the following formula:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\lambda$ is the mean in the given interval, which is the same as the variance.

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The normal approximation can be used to a Poisson distribution, with $\mu = \lambda, \sigma = \sqrt{\lambda}$

Computer Help Hot Line receives, on average, 14 calls per hour asking for assistance.

This means that $\lambda = 14$ .

Then

$\mu = 14, \sigma = \sqrt{14} = 3.74$

What is the probability that the company will receive more than 20 calls per hour?

Using continuity correction, this is P(X 20 + 0.5) = P(X 20.5) , which is 1 subtracted by the pvalue of Z when X = 20.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{20.5 - 14}{3.74}$

Z = 1.74

Z = 1.74 has a pvalue of 0.9591

1 - 0.9591 = 0.0409

0.0409 = 4.09% probability that the company will receive more than 20 calls per hour

Answer from: Quest

yes

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8. 4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

Answer from: Quest

0.6

39mph

step-by-step explanation:

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