SOLUTION: Customers arrive at a local ice cream stand at an average rate of 16 per hour. a. What is the probability that 2 customers will arrive during the next 15 min

Question 1061748: Customers arrive at a local ice cream stand at an average rate of 16 per hour.

a. What is the probability that 2 customers will arrive during the next 15 minutes?
b. What is the probability that 4 customers will arrive during the next 15 minutes?
c. What is the probability that 6 customers will arrive during the next 30 minutes?
d. What is the probability that more 7 customers will arrive during the next 45 minutes?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
P(x)=e(-lambda)*lambda^x/x! Poisson distribution--discrete, proportional, could be infinite theoretically
lambda=16 or 4 per quarter hour
P(2)=0.1465. That is e^(-4)(4^2)/2!
P(4)=0.1954
P(6), now lambda is 8; 0.1221
7 more (if that is the intent of the question) is a lambda of 12. If it is more than 7, it is longer to do but it's done the same way using the formula above. From the table, more than 7=0.9105.
e^(-12)*12^7/7!
=0.0437

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