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.

step-by-step explanation:

3,6 and 7.

step-by-step explanation:

a) unit place of 37 is 7

so the unit place of cube of 37 will be

7³= 343=3

the answer is 3.

b) unit place of 56 is 6, so the unit place of cube of 56 will be

6³= 216=6

the answer is 6.

c) unit place of 133 is 3, so the unit place of cube of 133 will be

3³= 27= 7.

the answer is 7.