It\'s a football game night in Stillwater and that means tons of people are orde
ID: 3182672 • Letter: I
Question
It's a football game night in Stillwater and that means tons of people are ordering pizza. A delivery driver at Hideaway Pizza is getting ready for their next delivery run. The driver has been given 5 different orders to deliver on the next driving run. The driver has been having a bit of car trouble and it has become such that the probability that their car can make it to the address of a given order without stalling out (the engine stopping) is 0.8. Assume that the orders are completely independent of each other as far as the car is concerned and that this probability of stalling remains the same from order to order. (a) What is the probability that the driver makes it to all orders without the car stalling out? (b) If the car stalls out on more than one order, the driver will end up being late delivering orders and customers will have to be compensated for getting a late pizza. What is the probability of this occurring? (c) What are the mean and standard deviation for the number of orders that the car will not stall out on while driving to the address for those orders?Explanation / Answer
Probability of car stalling = 0.2
a) probability that driver makes all the deliveries without engine stalling is =
number of orders to be delivered in this run = 5
hence probability of succesfull delivery(without stalling = 0.8)
For all 5 orders probability = 0.8 * 0.8 * 0.8 * 0.8 * 0.8 = 0.32768
b) probability if car stalling on more than ine order = 1 -( probability of car not stalling + probability of car stalling only 1 time)
probability of car not stalling = 0.32768
probability of car stalling only 1 time = 5C1 * 0.8 * 0.8 * 0.8 * 0.8 * 0.2 = 0.4096
threfore 1 - 0.4096 - 0.32768 = 1 - 0.73728 = 0.26272
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