Question 1

Production needs your help with analyzing how many cars should produce. Considering that car's monthly demand is normally distributed, with a mean of 852 and a standard deviation of 284, answer the following questions:

Question 1.1: How many cars should company have in stock in a given month if the company wants to have a 95% probability of fulfilling the demand?

Round your answer to the nearest integer.

Question 1.2:If company has an inventory of 1000 cars in a given month, what's the probability of stocking out (meaning that the demand for that month exceeds the number of cars in stock)?

Enter your answer as a decimal form with THREE decimal places.

Manager thinks that, maybe, copany should produce as many cars as possible to ensure all monthly demand is fulfilled. What is true about this approach?

Question 1.3:Select the correct answer.

- As company produces more cars above the mean of the distribution, the probability of those cars not being sold during the month is higher.

- The most likely outcomes of the Normal Distribution occur at the extremes, so it always makes sense to manufacture as many cars as possible.

- If the mean of the Normal Distribution was smaller, the shape of the distribution would be more flat, so manufacturing as many cars as possible would make sense.

Question 2

After-sales services are an essential part of company's strategy. Fauna owns vehicle repair shops in every city . For example, in Barcelona, each hour of the day several customers come to fix their cars at company's vehicle repair shop. This can be modeled as a Poisson distribution with lambda () = 4.7 cars per hour.

Question 2.1:Given this Poisson distribution, what is the probability that the number of cars that company's vehicle repair shop in Barcelona receives in one hour will be greater than 3?

Enter your answer as a decimal form with THREE decimal places. For example, if your answer is 76.06%, you should enter 0.761 in the answer box.

Question 2.2: If lambda () decreases to 0.7, how will the Poisson distribution change?

- The distribution could take negative values, as Lambda is less than 1.

- The distribution will be more asymmetric.

- Smaller values would appear less frequently than before.

Question 3

Component Y1 is crucial for company's vehicle repair shops, as it is one of the components that fails most often in company's cars. For this component, the monthly demand in company's vehicle repair shop in Barcelona follows a continuous uniform distribution with a minimum value of 4 units and a maximum of 17 units. Considering this information, answer the following questions:

Question 3.1: What is the probability that company's vehicle repair shop in Barcelona will be able to fulfill the monthly demand of component Y08 if it has 12 units in stock?

Enter your answer as a decimal form with THREE decimal places.

Question 3.2:What is the coefficient of variation of this continuous uniform distribution?

Enter your answer as a decimal form with THREE decimal places. For example, if your answer is 76.06%, you should enter 0.761 in the answer box.

Question 3.3:What is the probability of the monthly demand being between +/- 0.5 standard deviation of the average demand for the component Y08?

Question 4

company knows that not all their cars are perfectly manufactured. Some cars present small imperfections that can be fixed at the end of the production line, and some cars present issues that need repair and must go through an internal repair station.

company currently produces batches of 100 cars. The company has gathered the following information about the distribution of cars, on average, in every batch of 100 cars.

Needs Repair	Small Imperfections	Perfectly Manufactured
7	6	87

An external auditor is coming to Fauna's manufacturing plant to evaluate how good company's manufacturing process is. The auditor will be analyzing a single batch, and he will be selecting two different cars at random from this batch. Considering this, Brenda wants to know the following:

Question 4.1:What is the probability that the first car analyzed by the auditor isnotPerfectly Manufactured?

Enter your answer as a decimal form with THREE decimal places.

Question 4.2:If the first car analyzed by the auditor was a car that Needs Repair, what's the probability that the second car analyzed by the auditor isnotPerfectly Manufactured? (Note: Assume that the auditor will never select the same car for review again.)

Enter your answer as a decimal form with THREE decimal places.