Astatistics professor finds that when he schedules an office hour at the 10: 30 a. m. time slot, an average of three students arrive. use the poisson distribution to find the probability that in a randomly selected office hour in the 10: 30 a. m. time slot exactly five students will arrive.

Using poisson distribution the probability that in a randomly selected office hour in the 10:30 a.m. time slot exactly five students will arrive is 0.10

Solution:  

The professor expected the students will arrive at 10:30 pm

The average of students arrive in time = 3

By using poisson equation,

A Poisson distribution is a statistical distribution showing the likely number of times that an event will occur within a specified period of time. It is used for independent events which occur at a constant rate within a given interval of time.

where is mean or average.

For exactly 5 students , x = 5 and = 3

We know that

Hence,

Hence using poisson distribution the probability that in a randomly selected office hour in the 10:30 a.m. time slot exactly five students will arrive is 0.10

i think the answer would be c