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

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.