Mathematics, 23.03.2020 21:31 kailahgranger

G The average number of oil tankers arriving each day at a certainport city is 10. The facilities at the port can handle at most15 tankers per day. What is the probability that on a given daysome tankers have to be turned away

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Answer from: wickedskatboarder

2.87% probability that on a given day some tankers have to be turned away

Step-by-step explanation:

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

Poisson distribution:

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

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

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

Normal distribution:

Problems of normally distributed samples are solved using 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 Poisson distribution can be approximated to the normal with mean $\mu$ and standard deviation $\sigma = \sqrt{\mu}$ .

The average number of oil tankers arriving each day at a certainport city is 10.

This means that $\mu = 10$

The facilities at the port can handle at most15 tankers per day. What is the probability that on a given daysome tankers have to be turned away

So at least 16 tankers, which is 1 subtracted by the pvalue of Z when X = 16.

$\sigma = \sqrt{10} = 3.1623$

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

$Z = \frac{16 - 10}{3.1623}$

Z = 1.90

Z = 1.90 has a pvalue of 0.9713

1 - 0.9713 = 0.0287

2.87% probability that on a given day some tankers have to be turned away

Answer from: Quest

ik how do do this just give me a few minutes and i will give it to

Answer from: Quest

the car was traveling 40 mph before it started skidding. ( 2 points ) 17. was the driver were her brakes working at 75% efficiency or better? ( 2 points ) yes 29.

step-by-step explanation:

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