Reference no: EM132854232

You own a parkade with 100 parking spots. Over morning rush hour (between 6:00 am and 9:00 am), there are on average 95 cars that come looking for a parking space. 70% of the people that come to the parkade have parking passes.

Question 1: After opening the parking lot at 6:00 am, you realize you forgot your coffee at home. If you grab a coffee across the street, it will take 10 minutes. What is the probability that 1 or more cars will come over the 10 minutes it takes to get a coffee?
What kind of distribution should you use for this problem?

-Binomial
-Poisson
-Not enough information to answer
-Neither Poisson nor Binomial

Question 2: You went and got the coffee and noticed 3 cars turn into the parking lot while you were getting your coffee. There is no automated gate at your parking lot. Cars simply enter freely and either show you their pass or pay you as they enter. What is the probability that at least one of the 3 cars that entered the parking lot did NOT have a parking pass?
What kind of distribution should you use for this problem?

-Binomial
-Poisson
-Not enough information to answer
-Neither Poisson nor Binomial

Question 3: You are a server at a restaurant where the food-safety practices are... questionable may be the polite way of putting it. On average, 1 hair is found in the food every hour. The number of hairs found in food follows a Poisson distribution.

You are interested in the probability that there will be exactly 1 hair found in food over the next hour. Answer the following questions for the analysis:

a) What λ-value should you use?

b) What is/are the x-value(s) for which you are assessing the probability?

-x = 0
-x > 1
-x = 1
-x >= 1c) What is the probability EXACTLY 1 hair will be found in food over the next hour?

P(Exactly 1 hair) = (answer as decimal, rounded to 4 decimal places)

Question 4: You are working a 4 hour shift and have a bet going with another server over how many hairs you'll find. You have bet that there will be 5 or more hairs found in food, whereas the other server has bet there will be less than 5 hairs found in food.
To determine the probability you are will win the bet (5 or more hairs found in food), what λ-value should you use?

Question 5: A towing service receives averages 4 requests per hour.

a) In any given hour, what is the probability they receive exactly five requests for assistance?

(Answer in decimal form, rounded to 4 decimals)

b) The operators of the towing service take a 45-minute break for lunch. How many requests for assistance would the towing service expect to receive over the 45 minute lunch break?

(Answer in decimal form, rounded to 4 decimals)

c) What is the probability they receive no requests for assistance over the lunch break?

(Answer in decimal form, rounded to 4 decimals)

d) What is the probability they will miss at least one request for assistance over the break?

(Answer in decimal form, rounded to 4 decimals)