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

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:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

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 and standard deviation , the zscore of a measure X is given by:

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 and standard deviation .

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

This means that

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.

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

step-by-step explanation:

y=mx+b

step-by-step explanation:

m slope

b y-intercept