A bakery sees an average of 10 customers per hour What is th

A bakery sees an average of 10 customers per hour. What is the probability that the waiting time for the next customer will be less than 10 minutes? (Round your answer to the nearest thousandth.)

Solution

mu = 10

P(x < 10) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6)
+ P(x = 7) + P(x =8) + P(x = 9)

= e^(-10)*(10)^0/0! + e^(-10)*(10)^1/1! + e^(-10)*(10)^2/2! + e^(-10)*(10)^3/3! +e^(-10)*(10)^4/4! + e^(-10)*(10)^5/5! + e^(-10)*(10)^6/6! + e^(-10)*(10)^7/7! + e^(-10)*(10)^8/8!
+ e^(-10)*(10)^9/9!
= 0.811(Ans.)