The number of hits on a certain website follows a Poisson distribution with a mean rate of 4 per minute. (a.) What is the probability that 5 hits are received in a given minute? (b.) What is the probability that 9 hits are received in 1.5 minutes? (c.) What is the probability that fewer than 3 hits are received in a period of 30 seconds?

a) 15.63% probability that 5 hits are received in a given minute.

b) 6.88% probability that 9 hits are received in 1.5 minutes.

c) 67.67% probability that fewer than 3 hits are received in a period of 30 seconds.

Step-by-step explanation:

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

is the Euler number

is the mean in the given time interval.

(a.) What is the probability that 5 hits are received in a given minute?

Mean rate of 4 per minute, which means that

This is P(X = 5).

15.63% probability that 5 hits are received in a given minute.

(b.) What is the probability that 9 hits are received in 1.5 minutes?

Mean rate of 4 per minute, so for 1.5 minutes,

This is P(X = 9).

6.88% probability that 9 hits are received in 1.5 minutes.

(c.) What is the probability that fewer than 3 hits are received in a period of 30 seconds?

Mean rate of 4 per minute, so for 30 seconds = 0.5 minutes,

This is

In which

So

67.67% probability that fewer than 3 hits are received in a period of 30 seconds.

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step-by-step explanation:

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