Mathematics: Records show that the average number of job applications received per week is 5.9. Find the probability of 6 job applications received in a given week.

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Records show that the average number of job applications

madmatt873

20.01.2022

16.05% probability of 6 job applications received in a given week.

Step-by-step explanation:

When you have the mean during an interval, you should use the 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 interval.

Records show that the average number of job applications received per week is 5.9.

This means that $\mu = 5.9$

Find the probability of 6 job applications received in a given week.

This is P(X = 6).

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

$P(X = 6) = \frac{e^{-5.9}*(5.9)^{6}}{(6)!} = 0.1605$

16.05% probability of 6 job applications received in a given week.

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