Part 1 - 10 materials samples have been tested, with their Yield Strengths being recorded. This data is available on Blackboard, along with a script to load the data.

1. Determine the sample mean and variance for the Yield Strengths using MATLAB.

2. Determine the 95% confidence interval for the Yield Strength of the material.

3. The materials supplier claims that the material has a Yield Strength of 200 MPa. Conduct a hypothesis test to see if there is sufficient evidence to suggest that this Yield Strength is incorrect. Use the comparison between T test and tN-1, 1-α/2 for your hypothesis test.

4. If the sample mean and variance stayed the same, but there were 50 samples to test instead of 10, do we get the same result from the hypothesis test? Explain your result.

Part 2 - Statistics were gathered on the traffic through a street. It is your job to determine the probability of certain events with the use of probability distributions. Make sure that all answer are solved by hand and are verified using MATLAB (code must be provided).

1. During the testing time, it was found that cars pass by at an average rate of 100 per hour, and the time at which cars passed was independent. What is the probability that there will more than 2 cars passing through in 1 minute?

2. What is the probability that the time between two cars is less than 1 minute?

3. What is the probability that there will be less that 1 minute between cars four times in a row?

4. The speed of cars has been found to be approximately normally distributed. The average speed of a car is 60km/h, while the variance is 5km2/h2 . Given a speeding fine will be given to those over 63km/h, what is the probability of a random car getting a speeding fine?

5. What is the probability that there are less than two speeding fines given in 15 minutes?