Question

please provide an explanation for your answer.

PLEASE SHOW WORK TO GET FULL UI Problem 2) This problem two independent parts a) and b) a) The number of cars arriving at a fast food drive-through is modeled by a Poisson distribution with an average of 8 cars per hour. What is the nmhability that fewer than 2 cars arrive at the fast food drive-through per 30 minutes. (5 points) (Round

Answer 1

a)

expected number of cars in 30 minutes =8*30/60 =4

therefore P(fewer than 2 cards) =P(X<=1 )=P(X=0)+P(X=1)=e^-4*4⁰/0!+e^-4*4¹/1!=0.0916

b)

here as median =ln(2)/$\lambda$ =4

therefore $\lambda$ =ln(2)/4

P(X>5 )=e^-$\lambda$x =e^-ln(2)*5/4 =(1/2)^5.4 =0.4204 ~ 0.42 option (iv) is correct