SOLUTION: Clients enter a tax​ preparer's office at an average rate of 8 per hour. They enter randomly and independently of one another. Express your answers to four decimal places.

Algebra ->  Probability-and-statistics -> SOLUTION: Clients enter a tax​ preparer's office at an average rate of 8 per hour. They enter randomly and independently of one another. Express your answers to four decimal places.       Log On


   



Question 1085112: Clients enter a tax​ preparer's office at an average rate of 8 per hour. They enter randomly and independently of one another.
Express your answers to four decimal places. Express the probabilities as decimal fractions​ -- not as percentages.
a. What is the probability that exactly 7 clients will enter the office in the next half​ hour?
nothing
b. What is the probability that at least one client enters the office in the next half​ hour?
nothing
c. What is the mean of the number of clients who will enter the office in the next half​ hour?
nothing
d. What is the variance of the number of clients who will enter the office in the next half​ hour?

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
This would be a Poisson distribution with mean 4 for a half hour
Therefore,
c=4 people
d=4 people^2, since Poisson has mean=variance.
Probability of 7 is e^(-4)*4^7/7!=0.0595
probability of 0 clients is e^(-4)=0.0183
1-0.0183=0.9817; this is the probability of at least 1 client.